instruction stringlengths 1.03k 9.61k | input stringclasses 1
value | output stringlengths 544 10.1k |
|---|---|---|
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem is a linear programming (LP) problem. We need to decide the quantities of DrugA and DrugB (continuous variables) to maximize total efficacy, subject to a budget constraint, a minimum patient coverage constraint, and a storage capacity constraint. All parameters are given in the problem statement.
</... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
**Modeling check**
- Variables: continuous (per prompt: "nonnegative continuous numbers").
- Objective: maximize total MWh (linear).
- Constraints: land (acres) and capital (thousands $) both ≤.
- No ratio constraints.
</think>
<model>
**Sets**
None (individual variables)
**Parameters**
- Land available: 500 ... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Product-mix linear program. Variables: number of veggie wraps (veggie) and chicken wraps (chicken). Since wraps are indivisible units, variables should be integer. Objective: maximize total profit. Constraints: preparation time, cooking time, cooler capacity. All constraints are linear and direction is correct.... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Bottles are indivisible items, so standard and premium should be integer variables. The objective is to minimize total molding time: 4*standard + 6*premium. Constraints: resin capacity (2*standard + 5*premium <= 800), dye capacity (3*standard + 1*premium <= 600), and premium ratio (premium >= 0.4*(standard + pr... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>The problem asks how many small and large carriers to use. Carriers are indivisible units, so the decision variables must be integer. Each small carrier holds 4 animals, each large carrier holds 10. There are at most 60 carriers total, the number of small carriers must be at least three times the number of large... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
We need to decide the number of standard containers (S) and refrigerated containers (R) to maximize total cargo weight. Each standard container carries 20 tons and uses 3 liters of fuel; each refrigerated container carries 40 tons and uses 2 liters of fuel. Total fuel available is 150 liters. At least 10 refrig... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check:
- Variables: P (primary hubs) and S (secondary hubs) are counts of hubs, indivisible, so INTEGER type.
- Objective: minimize total transit time = 4*P + 6*S (hours per unit times number of hubs; note transit time per unit is given, total transit time is linear in P and S).
- Constraints: (1) 50*P... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>The problem involves maximizing monthly profit from processing plastic and glass waste. We have two resources: shredder and washer, each with a capacity of 2000 hours per month. Plastic requires 2 shredder hours and 1 washer hour per ton, while glass requires 1 shredder hour and 3 washer hours per ton. Profit pe... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
We need to decide how many standard and express packages to deliver to maximize total delivery value, subject to weight and volume capacities. This is an integer linear programming problem because packages are indivisible units. Decision variables are integer and nonnegative. The objective is linear, and both c... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>The problem is to maximize total profit from producing standard and ergonomic chairs subject to cutting and assembly machine time limits. Since chairs are indivisible units, we define integer decision variables for the number of each chair type produced daily. The objective is to maximize 12 * x_standard + 18 * ... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
**Modeling check:**
- Variables: chairs and tables are discrete items (counts), so integer type is appropriate. The prompt does not explicitly say continuous, so integer is correct.
- Objective: minimize total cost, linear.
- Constraints: wood and metal limits are ≤; table share limit is ≤ 40% of total producti... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
We need to determine the optimal generation levels (in MWh) for gas turbine, hydro, and solar generators to maximize total revenue, subject to a minimum total power demand of 600 MWh, a total fuel availability of 3000 units, and a requirement that at least 25% of total power comes from renewable sources (hydro ... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: This is a product mix problem with indivisible items (kits). Decision variables should be integer (counts). Objective is to maximize profit. Constraints: reagent A limit (2*rapid + 1*pcr ≤ 500), reagent B limit (1*rapid + 3*pcr ≤ 600), packaging limit (rapid ≤ 200). All constraints are linear. N... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
We need to decide how many liters of standard paint (standard) and premium paint (premium) to produce. The objective is to minimize total binder usage: 3*standard + 2*premium. Constraints: pigment limit (2*standard + 5*premium <= 4000), binder limit (3*standard + 2*premium <= 3000), at least 60% premium (premiu... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem involves minimizing total storage cost for two types of medical kits (basic and advanced) subject to space capacity, labor hours, and minimum demand constraints. The decision variables are the quantities of basic and advanced kits to stock. Since kits are indivisible units, the variables should be i... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem involves allocating capital across three asset classes (stocks, bonds, commodities) to maximize total expected profit, subject to a capital budget and a risk limit. The decision variables are the number of units invested in each asset class. Since units are indivisible, the variables should be integ... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: This is a cost-minimization linear program. Decision variables are the number of bags of each blend. Bags are indivisible, so variables should be integer (GRB.INTEGER). Objective: minimize total cost. Constraints: nitrogen and phosphorus minimum requirements (≥), potassium maximum limit (≤). All... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
**Modeling check**
- Variables: matte, gloss (continuous, liters) – divisible quantity, no integer requirement in prompt.
- Objective: minimize 4*matte + 6*gloss (solvent usage).
- Constraints: pigment (2*matte+3*gloss ≤ 6000), binder (5*matte+4*gloss ≤ 8000), gloss share (gloss ≥ 0.4*(matte+gloss) → 0.6*gloss ... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem involves deciding the number of organic waste digesters (D) and plastic-to-fuel converters (C) to maximize total daily waste processed. Each digester processes 40 tons and requires 2 operators; each converter processes 25 tons and requires 3 operators. The city has 2000 tons daily waste capacity and... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
We need to minimize total protein usage. Let regular_chews be the number of regular chews and premium_chews be the number of premium chews. The objective is 5*regular_chews + 7*premium_chews. Constraints: dental paste limit 8*regular_chews + 12*premium_chews <= 4800, at least 40% regular: regular_chews >= 0.4*(... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: This is a product-mix problem with indivisible units (cabinets). Decision variables are integer counts. Objective is linear cost minimization. Constraints are linear resource limits and a minimum production requirement. No ratio constraints. Gurobi 12.x API used correctly.
</think>
<model>
**Se... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: hay bales and grain sacks are indivisible items (counts), so variables should be integer. Objective is to maximize total cost. Constraints: fiber requirement (≥600), protein requirement (≥320), storage limit (≤100). All constraints are linear. No ratio constraints.
</think>
<model>
### Sets
None... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem involves minimizing total labor used to produce steel beams and aluminum frames, subject to material and labor availability, a minimum production requirement for beams, and a ratio constraint between frames and beams. The decision variables are the number of beams and frames, which are discrete coun... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>We need to decide how many Veggie Wraps and Chicken Wraps to produce to maximize profit, subject to limited resources (tortilla, vegetables, chicken, sauce). This is a linear programming problem. Since wraps are indivisible items, the decision variables should be integer.
Modeling check:
- Variable type: intege... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check:
- Variables: standard and deluxe chairs are integer (indivisible units).
- Objective: minimize total labor hours (linear).
- Constraints: wood limit, labor limit, deluxe ratio (linearized as deluxe >= 0.4*(standard+deluxe)).
- Ratio constraint is linear after multiplying both sides.
</think>
<m... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
We need to decide how many brackets and flanges to produce. The objective is to minimize total material waste. The constraints are: steel and laser cutting capacity, at least 40% of total output must be flanges, and at least 50 brackets must be produced. This is a linear programming problem with two integer var... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: variables are integer (batches are indivisible). Objective minimizes total pigment units (8 per interior batch, 9 per exterior batch). Constraints: pigment availability (≤), interior ratio (≥30% of total), exterior ≥ 2× interior. Ratio constraint linearized as 0.7*interior - 0.3*exterior ≥ 0.
</... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: decision variables are chair counts (indivisible) → integer type. Objective: minimize total cost (linear). Constraints: wood and labor are linear resource limits; deluxe ratio constraint is linearized as deluxe >= 0.4*(standard+deluxe) → 0.6*deluxe >= 0.4*standard. Gurobi 12.x API used correctly... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem is a classic resource allocation linear program. We need to decide how many acres to plant with wheat and how many with barley to maximize total bushels, subject to land, fertilizer, and water constraints. The decision variables are continuous (acres). The objective is to maximize 12 * wheat_acres +... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check:
- Variables: S (standard chairs) and D (deluxe chairs) are counts of indivisible items, so they should be integer (GRB.INTEGER).
- Objective: minimize total cost = 5*(2S+3D) + 20*(1S+2D).
- Constraints: exact usage of wood (2S+3D=150) and labor (1S+2D=80).
- No ratio or percentage constraints.
<... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: Decision variables are counts of discrete items (steel beams, aluminum frames) so they must be integer. Objective is to minimize total production time (minutes). Constraints: steel, aluminum, labor limits (≤), minimum production requirements (≥). All constraints are linear. No ratio constraints.... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: decision variables are counts of vans (indivisible) so integer domain is appropriate. Objective is linear maximization of total packages. Constraints include availability, driver hours, total vans, minimum express, and ratio E ≤ 0.5*S (linear). All constraints are linear and suitable for Gurobi ... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>Modeling check: variables are counts of nurses (indivisible) → INTEGER. Objective: maximize 8*day + 5*night (linear). Constraints: patient coverage (≥), total nurses (≤), day limit (≤), night ratio (≥ 0.4 of total). Ratio constraint linearized: night ≥ 0.4*(day+night) → 0.6*night ≥ 0.4*day → 3*night ≥ 2*day. All... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>The problem asks for the number of units of each formulation to select. Units are indivisible counts, so the decision variables should be integer. The objective is to maximize total therapeutic efficacy, which is linear. The constraints are linear: an upper bound on active ingredient usage and lower bounds on ef... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
We need to minimize total raw material cost for producing chairs and tables. Chairs and tables are discrete items, so variables should be integer. Each chair uses 4 wood and 2 metal; each table uses 6 wood and 5 metal. Wood cost $2/unit, metal $3/unit. Available: 240 wood, 180 metal. At least 20 chairs and 10 t... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
We need to maximize profit from producing two types of vaccine batches subject to reagent limits and safety constraints. The decision variables are the number of Adenovirus batches (adenovirus) and Lentivirus batches (lentivirus). Since batches are indivisible, variables should be integer. The objective is to m... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: Batches are indivisible units, so variables should be integer (not continuous). Objective is to maximize total sanitizer volume. Constraints are linear resource limits and a ratio constraint on Premium batches. The ratio constraint x_prem ≤ 0.4*(x_std + x_prem) simplifies to 3*x_prem ≤ 2*x_std, ... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: variables A and B are continuous (batches can be fractional). Objective is maximize A+B (linear). Constraints: raw material 4A+6B≤2000, mixing time 2A+B≤600, ratio B≤0.6(A+B) linearized to B≤1.5A, minimum A≥30. All constraints linear, Gurobi 12.x compatible.
</think>
<model>
**Sets**
None (two ... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
We need to determine the optimal liters of matte and gloss paint to produce. The objective is to minimize total pigment usage (pigment A + pigment B). Matte uses 2 units of pigment A per liter, gloss uses 3 units of pigment B per liter. Constraints: pigment A availability (500 units), pigment B availability (60... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>We need to maximize total patient coverage by deciding how many saline, electrolyte, and nutrient bags to produce, subject to ingredient availability and a requirement that electrolyte bags constitute at least 25% of total production. Bags are indivisible items, so integer variables are appropriate. The objectiv... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: decision variables are integer (count of chairs, indivisible). Objective minimizes linear cost. Constraints: wood and fabric are upper bounds, demand is lower bound, contract ratio is lower bound. Ratio constraint x_p >= 0.5 x_s is linear and valid.
</think>
<model>
**Sets**
None (single-period... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
This is a linear programming (LP) blending problem. Decision variables are liters of Solution A and Solution B, which are continuous (divisible). Objective is to maximize total nutrient units. Constraints: ingredient availability (upper bounds) and minimum nutrient requirements (lower bounds). All coefficients ... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
We need to maximize total power output from three generator types (gas, coal, hydro) subject to limits on fuel, cooling water, and heat emissions. The decision variables are the MWh produced by each generator. The objective coefficients are the power output values per MWh. The constraints are linear resource li... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: Decision variables x_A and x_B represent number of doses, which are indivisible counts. Therefore they should be integer (GRB.INTEGER). Objective is linear maximization. Constraints are linear. The ratio constraint x_B <= 0.4 (x_A + x_B) linearizes to 0.6 x_B - 0.4 x_A <= 0. All constraints are ... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: Decision variables are counts of parcels (indivisible units), so they must be integer. Objective is to maximize total profit. Key constraints: cargo space capacity (linear), express ratio (linearized to express_parcels >= 0.3 * total), budget (linear). All constraints are linear, suitable for LP... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
We need to maximize profit from producing pediatric and adult liquid medication formulations. The decision variables are liters of pediatric (P) and adult (A) formulations. The objective is to maximize 12P + 18A. Constraints: active ingredient limit (10P + 15A ≤ 5000), mixing tank capacity (P + A ≤ 400), minimu... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem is a classic blending/linear programming problem. We need to decide the liters of SalineX and NutriY to minimize cost while meeting minimum requirements for sodium, potassium, and glucose. The data is given directly in the problem statement.
Decision variables:
- SalineX: liters of SalineX solution... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
**Modeling check**
- Variables: gas_turbine, steam_turbine (continuous, nonnegative). Electricity output (MWh) is divisible, so continuous is correct.
- Objective: minimize total fuel consumption (linear).
- Constraints: demand (≥), fuel budget (≤), water budget (≤), minimum steam ratio (≥). The ratio constrain... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem involves minimizing the total binder used in producing premium and standard paint, subject to minimum pigment and binder requirements and a ratio constraint on premium paint. The decision variables are continuous liters of each paint type. The objective is to minimize 2*premium + 3*standard. Constra... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: variables are counts of containers (indivisible) so integer domain is appropriate. Objective is maximize profit. Key constraints: weight capacity (≤), volume capacity (≤), minimum total containers (≥), minimum refrigerated containers (≥). No ratio constraints. Linear model, Gurobi 12.x compatibl... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem is to minimize the total cost of purchasing Organic and Synthetic fertilizer bags while meeting minimum nutrient requirements and a ratio constraint. The decision variables are the number of bags of Organic (organic) and Synthetic (synthetic). Since bags are indivisible, both variables should be int... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem is to minimize total promotional cost while meeting minimum exposure requirements for two demographics. The decision variables are the number of units for social media, email, and display advertising. The objective is to minimize 4.2*social + 6.8*email + 5.5*display. The constraints ensure at least ... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem involves minimizing the total amount of nutrient concentrate used while preparing saline and nutrient IV bags, subject to resource constraints and demand conditions. The decision variables are the number of saline bags (saline) and nutrient bags (nutrient). Since bags are indivisible, both variables... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: Variables are continuous (liters of biodiesel, divisible quantity). Objective minimizes total catalyst usage (linear). Constraints: palm oil capacity (≤), soybean oil capacity (≤), minimum production (≥). No ratio constraints. LP model, Gurobi 12.x compatible.
</think>
<model>
**Sets**
None
**P... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
We need to minimize total fuel consumption subject to a minimum delivery requirement, a fuel budget, and a constraint that the number of large vessel trips does not exceed the number of small vessel trips. The decision variables are the number of trips for each vessel type, which are nonnegative integers (trips... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: decision variables are integer (counts of tests), objective is minimization of total waiting time, constraints are linear nurse and equipment capacity with lower bounds.
</think>
<model>
**Sets**
- None (scalar problem)
**Parameters**
- nurse_basic = 15 (minutes per basic test)
- equip_basic =... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>The problem involves deciding how many type A and type B IV bags to produce to minimize total fluid consumption, subject to fluid availability, minimum demand, and a ratio constraint. The decision variables are integer (number of bags). The objective is to minimize the sum of fluid A and fluid B used. Constraint... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
We need to determine the optimal number of Antibiotic and Hydration IV bags to maximize profit, subject to resource constraints and a minimum production requirement. This is a linear programming problem with two integer decision variables: the number of Antibiotic bags (A) and the number of Hydration bags (H). ... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem is a linear programming (LP) model. We have three continuous decision variables: wind, solar, and hydro units. The objective is to maximize total profit: 4 * wind + 3 * solar + 5 * hydro. The constraints are: capital budget (2*wind + 1.5*solar + 3*hydro <= 100), land area (3*wind + 2*solar + 4*hydro... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
We need to maximize total expected return by deciding how many millions to invest in stocks, bonds, and real estate. Each investment consumes analyst hours and risk units, and we have limited resources. This is a linear programming problem with continuous variables.
</think>
<model>
**Sets**
None (three indivi... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem is to maximize total profit from producing standard and enhanced vaccine vials. Decision variables: x_standard (number of standard vials) and x_enhanced (number of enhanced vials). Since vials are indivisible units, variables should be integer. Objective: maximize 12*x_standard + 18*x_enhanced. Cons... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>The problem involves maximizing profit from processing three types of parcels (small, medium, large) subject to sorting and loading time constraints. The decision variables are the number of each parcel type to process. Since parcels are indivisible units, the variables should be integer. The objective is to max... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem involves allocating cargo weight to vans and trucks to maximize profit, subject to fleet capacity and minimum cargo requirements. The decision variables are continuous kilograms allocated to each vehicle type. The objective is to maximize total profit, and constraints include fleet capacity limits, ... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check:
- Variable type: integer (IV bags are indivisible units; problem asks "how many of each bag" and total bag limit is 200, implying whole bags).
- Objective sense: maximize total profit.
- Key constraints: saline capacity, tubing capacity, total bag limit.
- No ratio/percentage constraints.
</thin... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem is a fuel blending optimization. We need to determine the tons of Coalite and Ember to blend such that the blend meets minimum sulfur (≥4%), maximum ash (≤3.5%), and minimum heat content (≥85 units/ton) requirements, while minimizing total cost. Coalite costs $8/ton and Ember costs $11/ton. Coalite ... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
We need to assign nurses to three shifts (morning, afternoon, night) to meet minimum coverage requirements while minimizing total cost. Each nurse works at most one shift per day. The costs per nurse are $120, $150, and $200 for morning, afternoon, and night shifts respectively. Minimum nurses required are 8, 6... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>The problem is to maximize total carbon sequestration by selecting the optimal number of native forest projects and mangrove projects, subject to land, budget, and total project constraints. This is a linear programming problem with two integer decision variables: the number of native forest projects (native) an... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem involves minimizing the total cost of producing two intravenous fluids (A and B) while meeting minimum production volumes, protein and electrolyte requirements, and base solution supply limits. The decision variables are the liters of fluid A and fluid B to produce. The objective is to minimize tota... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Trips are indivisible counts, so decision variables must be integer. The objective is to maximize total containers. Constraints: fuel budget ($9000), max 12 electric trips, diesel trips at least 3 times electric trips. This is a small integer linear program.
</think>
<model>
**Sets**
None (scalar problem)
**Pa... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem involves three continuous decision variables (Alpha, Beta, Gamma production quantities). The objective is to maximize total profit. Constraints include resource capacities (reactor, blending, testing), minimum production commitments for Alpha and Beta, and a blending ratio that Gamma cannot exceed 3... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
This is a product mix optimization problem. The decision variables represent the number of chairs produced, which are indivisible units, so they should be integer. The objective is to maximize total profit subject to resource constraints. This is a linear integer programming problem.
</think>
<model>
**Sets**
... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
**Modeling check**
- Variables: D (day overtime hours) and N (night overtime hours) are continuous because hours are divisible quantities. The prompt does not require integer hours.
- Objective: minimize 12*D + 18*N (cost per hour).
- Key constraints: minimum patient care hours (D >= 200, N >= 120), nurse capac... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
**Modeling check**
- Variables: Mineral and Synthetic are continuous (divisible quantities, no integer requirement in prompt).
- Objective: minimize total cost, linear.
- Constraints: viscosity, flash point, and max Mineral fraction are linear after cross-multiplying; all are linear inequality constraints.
- Ra... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check:
- Variables: van_trips and truck_trips are counts of trips, so they should be integer (GRB.INTEGER). The prompt does not specify continuous, so integer is appropriate.
- Objective: minimize total fuel consumption (linear).
- Constraints: parcel delivery (≥600), truck ratio (truck_trips ≥ 0.4*(va... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: decision variables are counts of drivers (indivisible), so they must be INTEGER. Objective is minimization of total cost. Key constraints: package delivery (at least 1500) and day driver limit (at most 10). No ratio constraints.
</think>
<model>
**Sets**
None.
**Parameters**
- day_packages_per... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: trips are indivisible counts, so integer variables are appropriate. Objective is maximize total cargo (linear). Constraints: budget (≤), total trips (≤), minimum large trips (≥), fleet ratio (large ≤ 2× small). All constraints are linear. No ratio/percentage linearization needed.
</think>
<mode... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
**Modeling check**
- Variables: standard_nodes (integer, >=0), high_capacity_nodes (integer, >=0). Node counts are indivisible, so integer domain is required.
- Objective: maximize total throughput (linear).
- Constraints: throughput >= 1000 (linear), latency <= 50 (linear).
- No ratio or percentage constraints... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: variables are continuous (liters are divisible), objective is minimization, constraints are linear, ratio constraint Y >= 0.3*(X+Y) is linearized to 0.7*Y - 0.3*X >= 0.
</think>
<model>
**Sets**
None (individual variables)
**Parameters**
- chemA_per_X = 3 (units of chemical A per liter of Solve... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
We need to maximize total weekly profit by deciding how many express and standard routes to schedule. Express routes use 2 driver hours and 3 vehicle hours, earning $400 each. Standard routes use 4 driver hours and 1 vehicle hour, earning $250 each. Driver hours are limited to 1200 per week, vehicle hours to 90... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem involves two continuous decision variables: liters of standard solvent (standard) and liters of premium solvent (premium). The objective is to minimize total energy consumption: 2*standard + 3*premium. Constraints: chemical A usage (4*standard + 5*premium ≤ 12000), chemical B usage (3*standard + 2*p... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
**Modeling check**
- Variable domain: continuous (per prompt). Count-like but explicitly continuous.
- Objective: maximize total power output (linear).
- Constraints: land (≤), budget (≤), carbon credits (≥). All linear.
- No ratio/percentage constraints.
- Gurobi 12.x compatible: standard linear model, no nonl... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check:
- Variables: continuous (hectares are divisible).
- Objective: maximize linear carbon sequestration.
- Constraints: land (≤50 ha), budget (≤$200k).
- No ratio constraints.
</think>
<model>
**Sets**
None.
**Parameters**
- carbon_native = 120 (tonnes CO2e per hectare of native planting)
- carbon_... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
**Modeling check**
- Variables: Alpha and Beta are tons of alloy (divisible quantity) → CONTINUOUS, nonnegative.
- Objective: minimize total scrap used (linear).
- Constraints: scrap and ore availability (≤), Alpha ratio (≤ 0.4 of total), minimum Beta (≥ 50).
- Ratio constraint linearized: Alpha ≤ 0.4*(Alpha + ... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
We need to decide how many liters of Solvent X and Solvent Y to blend. The objective is to minimize total cost while meeting the minimum requirements for compounds A and B and the maximum limit for compound C. The decision variables are continuous and nonnegative. The constraints are linear, so we can solve thi... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
**Modeling check**
- Variables: A, B (liters of solvent, continuous, divisible quantity).
- Objective: maximize 50A + 80B (profit).
- Constraints: material limits (≤), minimum production (≥).
- No ratio/percentage constraints.
</think>
<model>
**Sets**
- None (scalar problem)
**Parameters**
- X_per_A = 3 (uni... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check:
- Variables: standard_boxes and reinforced_boxes are counts of boxes (indivisible units) → integer, not continuous.
- Objective: minimize total cost (2*standard + 4*reinforced) → MINIMIZE.
- Constraints: cardboard (≤1200), adhesive (≤400), reinforced ratio (≥30% of total), minimum standard (≥60)... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
**Modeling check**
- Variables: continuous (tons of food scraps and yard trimmings). Divisible quantity, no integer requirement.
- Objective: maximize profit (linear).
- Constraints: supply upper bounds (≤) and methane emission cap (≤).
- Ratio/percentage: none.
- Gurobi 12.x: standard LP, no nonlinear forms.
<... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: trips are indivisible counts, so flatbed_trips and refrigerated_trips must be integer (GRB.INTEGER). Objective minimizes total cost. Key constraints: budget (120*f + 200*r <= 6000), flatbed limit (f <= 15), refrigerated minimum (r >= f). No ratio linearization needed.
</think>
<model>
**Sets**
... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem involves two integer decision variables: the number of cotton rolls (cotton) and the number of polyester rolls (polyester). Rolls are indivisible units, so integer variables are appropriate. The objective is to minimize total machine hours: 2*cotton + 4*polyester. Constraints: cotton usage 5*cotton ... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: trips are indivisible counts, so S and R must be INTEGER (not CONTINUOUS). Objective minimizes total cost. Key constraints: delivery demand (150S+250R≥2000), refrigerated ratio (R≥0.4(S+R) linearized to 3R≥2S), and max standard trips (S≤8). Ratio constraint is linear, no nonlinear forms.
</think... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>We need to decide how many hectares to allocate to Project A and Project B to maximize total carbon sequestration. The problem provides all parameters directly: carbon sequestration per hectare (12 for A, 9 for B), cost per hectare (40 for A, 25 for B), land requirement (1 hectare each), seedling requirement (20... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem involves minimizing total production cost for steel beams and aluminum frames subject to resource constraints (steel, aluminum, machining hours), a minimum beam production requirement, and a limit on how many more frames than beams can be produced. The decision variables are the number of beams and ... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
This is a linear programming blending problem. Decision variables are liters of two mixtures (M1 and M2), which are continuous and non-negative. The objective is to minimize total cost. Biomarker X must not exceed 8.0 units, biomarker Y must be at least 6.0 units. All quantities are divisible (liters, units), s... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
The problem involves two continuous decision variables: hydro_mwh (MWh from hydro plant) and wind_mwh (MWh from wind farm). The objective is to maximize total profit: 55 * hydro_mwh + 45 * wind_mwh. Constraints: water consumption 8 * hydro_mwh <= 1200, wind capacity wind_mwh <= 180, emission limit 0.02 * hydro_... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check:
- Variables: containers, lids (continuous, non-negative). Although the problem mentions "number of containers/lids", the prompt does not explicitly require integer variables; continuous relaxation is acceptable for this LP.
- Objective: minimize 4*containers + 2*lids (total machine hours).
- Con... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: The problem asks for the number of solar units and wind units to deploy. Units are indivisible counts, so the decision variables should be integer (non-negative). The objective is to maximize total profit. Constraints: water consumption limit (4*solar + 3*wind <= 500), minimum energy requirement... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: Decision variables are counts of fiber and microwave links, so they must be integer (GRB.INTEGER). Objective minimizes total latency (2*fiber + 5*microwave). Constraints: budget (fiber + microwave <= 10000) and throughput (50*fiber + 20*microwave >= 2000). Both constraints are linear. No ratio c... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check: The problem asks for number of bags, which are indivisible counts. Therefore standard and fortified should be integer variables. The objective minimizes total electrolyte mix used (1 per standard, 3 per fortified). Constraints: saline base (2*standard + fortified <= 100), electrolyte mix (standa... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>
Modeling check:
- Variables: chairs and tables are counts of discrete items, so they should be integer (GRB.INTEGER). The prompt does not specify continuous, and the problem involves indivisible units.
- Objective: minimize total production cost, linear.
- Constraints: resource limits (wood, metal, labor) are u... | |
SYSTEM:
You are a helpful Assistant with expertise in operations research and the Gurobi solver. When the User provides an OR question, you will analyze it, build a detailed mathematical model, and provide Gurobi code compatible with the `gurobipy` package version 12.x installed in the current environment.
Your respons... | <think>We need to decide how many solar, wind, and geothermal plants to build to maximize total green energy credits, subject to land, capital, and grid capacity constraints. Since plants are indivisible units, the decision variables should be integer (number of plants). The problem asks "how many plants" which implies... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.