mcp-optimizer

# Linear Programming - Usage Examples ## Description Linear programming allows solving optimization problems with linear constraints and linear objective functions. ## Example Prompts for LLM ### Example 1: Production Problem ``` Help me solve a production problem using MCP Optimizer. I have a factory that produces two types of products: tables and chairs. - Producing one table requires 4 hours of work and 2 kg of material - Producing one chair requires 2 hours of work and 1 kg of material - Profit from a table is $30, from a chair - $20 - 40 hours of work and 20 kg of material are available per day Find the optimal number of tables and chairs to maximize profit. ``` ### Example 2: Diet Problem ``` Use MCP Optimizer to solve a diet planning problem. I need to create a diet from three foods: - Bread: 2g protein, 50g carbs, 1g fat per 100g, cost $3/kg - Meat: 20g protein, 0g carbs, 15g fat per 100g, cost $50/kg - Milk: 3g protein, 5g carbs, 3g fat per 100g, cost $6/kg Requirements: - Minimum 60g protein per day - Minimum 300g carbs per day - Maximum 50g fat per day Find the minimum cost diet. ``` ### Example 3: Transportation Problem ``` Solve a transportation problem using MCP Optimizer. A company has 3 warehouses and 4 stores: Warehouses (supply): - Warehouse A: 100 units - Warehouse B: 150 units - Warehouse C: 200 units Stores (demand): - Store 1: 80 units - Store 2: 120 units - Store 3: 100 units - Store 4: 150 units Transportation costs ($/unit): From A: [5, 8, 6, 9] From B: [7, 4, 5, 8] From C: [6, 7, 4, 6] Find the optimal delivery plan with minimum costs. ``` ### Example 4: Blending Problem ``` Help solve a fuel blending problem with MCP Optimizer. An oil refinery produces gasoline by blending 4 components: - Component A: octane rating 95, cost $4.5/liter - Component B: octane rating 87, cost $3.8/liter - Component C: octane rating 92, cost $4.2/liter - Component D: octane rating 98, cost $5.0/liter Requirements for the final gasoline: - Octane rating at least 91 - Production volume 1000 liters - Component A should be at most 40% of the blend - Component D should be at least 10% of the blend Find the optimal blend composition to minimize cost. ``` ## Request Structure for MCP Optimizer For all problems, use the following structure: ```json { "objective": { "sense": "maximize" | "minimize", "coefficients": {"variable1": coefficient1, "variable2": coefficient2} }, "variables": { "variable1": {"type": "continuous", "lower": 0, "upper": null}, "variable2": {"type": "continuous", "lower": 0, "upper": null} }, "constraints": [ { "expression": {"variable1": coefficient1, "variable2": coefficient2}, "operator": "<=", "rhs": right_hand_side } ] } ``` ## Typical Activation Phrases - "Solve a linear programming problem" - "Find the optimal solution for..." - "Maximize/minimize subject to constraints..." - "Help with production/resource/cost optimization" - "Create an optimal plan..."