mcp-optimizer

# Knapsack Selection Problems - Usage Examples ## Description Knapsack selection problems solve the optimal selection of items with limited capacity to maximize total value or minimize costs. ## Example Prompts for LLM ### Example 1: Classic Knapsack Problem ``` Help me solve a knapsack problem using MCP Optimizer. I have a backpack with 50 kg capacity and the following items for hiking: Items: - Tent: weight 8 kg, value 100 points - Sleeping bag: weight 3 kg, value 70 points - Food for 3 days: weight 6 kg, value 90 points - Water 5L: weight 5 kg, value 80 points - Stove: weight 2 kg, value 60 points - First aid kit: weight 1 kg, value 50 points - Flashlight: weight 0.5 kg, value 40 points - Spare clothes: weight 4 kg, value 30 points - Book: weight 1 kg, value 20 points - Camera: weight 2 kg, value 85 points Find the optimal set of items to maximize hiking utility. ``` ### Example 2: Investment Portfolio with Limited Budget ``` Use MCP Optimizer to select investment projects. A company has a budget of $10 million for investments in the following projects: Projects: - New production line: cost $3M, NPV $5M - Warehouse modernization: cost $2M, NPV $3.5M - IT system: cost $1.5M, NPV $2.8M - Marketing campaign: cost $1M, NPV $1.8M - Staff training: cost $0.5M, NPV $1.2M - Research & development: cost $4M, NPV $6M - Office expansion: cost $2.5M, NPV $3M - Process automation: cost $3.5M, NPV $4.5M Additional constraints: - Maximum 5 projects can be selected - IT system and automation are interdependent (both or neither) - Staff training is mandatory if new production line is selected Maximize total NPV while meeting all constraints. ``` ### Example 3: Cargo Container Optimization ``` Solve a container loading problem with MCP Optimizer. A shipping container has constraints: - Maximum weight: 25 tons - Maximum volume: 60 m³ Goods to ship: - Electronics: 2 tons, 5 m³, value $500,000 - Clothing: 1 ton, 8 m³, value $200,000 - Furniture: 5 tons, 15 m³, value $300,000 - Auto parts: 3 tons, 4 m³, value $400,000 - Books: 4 tons, 6 m³, value $150,000 - Toys: 1.5 tons, 10 m³, value $250,000 - Sports goods: 2.5 tons, 7 m³, value $180,000 - Appliances: 6 tons, 12 m³, value $600,000 Additional conditions: - Fragile goods (electronics, appliances) cannot be overloaded - Priority given to goods with high value per kg Maximize cargo value in the container. ``` ### Example 4: Restaurant Menu Planning ``` Help plan a restaurant menu with MCP Optimizer. The restaurant has constraints: - Food procurement budget: $10,000/week - Cooking time: maximum 200 hours/week - Refrigeration space: 50 m³ Menu dishes: - Steak: cost $80, time 0.5h, space 0.2 m³, profit $120 - Pasta: cost $20, time 0.3h, space 0.1 m³, profit $40 - Caesar salad: cost $30, time 0.2h, space 0.3 m³, profit $50 - Soup of the day: cost $15, time 0.4h, space 0.1 m³, profit $25 - Grilled fish: cost $60, time 0.4h, space 0.4 m³, profit $90 - Pizza: cost $40, time 0.3h, space 0.2 m³, profit $70 - Dessert: cost $25, time 0.2h, space 0.2 m³, profit $45 - Burger: cost $35, time 0.25h, space 0.3 m³, profit $55 Expected demand (portions/week): Steak: 50, Pasta: 120, Caesar: 80, Soup: 100, Fish: 60, Pizza: 90, Dessert: 70, Burger: 85 Maximize restaurant profit. ``` ### Example 5: Advertising Budget Optimization ``` Optimize advertising budget allocation with MCP Optimizer. Marketing department has: - Total budget: $5 million - Time constraint: 3 months until launch - Maximum 8 advertising channels Advertising channels: - TV advertising: cost $1.5M, reach 2M people, conversion 2% - Internet advertising: cost $800K, reach 1.5M, conversion 3.5% - Radio: cost $400K, reach 800K, conversion 1.5% - Outdoor advertising: cost $600K, reach 1M, conversion 1% - Social media: cost $300K, reach 1.2M, conversion 4% - Email marketing: cost $100K, reach 500K, conversion 5% - Search advertising: cost $500K, reach 800K, conversion 6% - Influencers: cost $700K, reach 600K, conversion 3% - Print media: cost $350K, reach 400K, conversion 1.2% - Trade shows: cost $900K, reach 200K, conversion 8% Constraints: - Must include internet advertising - TV and radio cannot be used simultaneously - Minimum 3 digital channels Maximize number of potential customers. ``` ### Example 6: Project Team Formation ``` Help form a project team with MCP Optimizer. IT project requires: - Salary budget: $200,000/month - Maximum 12 people in team - Project duration: 6 months Available specialists: - Senior developer: $20K/month, skills 95 points, experience 8 years - Middle developer: $12K/month, skills 75 points, experience 4 years - Junior developer: $7K/month, skills 50 points, experience 1 year - Architect: $25K/month, skills 90 points, experience 10 years - DevOps engineer: $18K/month, skills 80 points, experience 5 years - Tester: $10K/month, skills 70 points, experience 3 years - UI/UX designer: $13K/month, skills 85 points, experience 4 years - Analyst: $14K/month, skills 75 points, experience 5 years - Project manager: $16K/month, skills 80 points, experience 6 years - Technical writer: $9K/month, skills 60 points, experience 2 years Requirements: - Minimum 1 architect - Minimum 3 developers - Mandatory 1 project manager - Senior:Middle:Junior ratio = 1:2:1 Maximize total team skill level. ``` ### Example 7: Production Program Optimization ``` Optimize production program with MCP Optimizer. Factory has constraints: - Working time: 2000 hours/month - Raw material A: 5000 kg/month - Raw material B: 3000 kg/month - Storage space: 1000 m² Products: - Product 1: time 2h, material A 5kg, material B 2kg, space 1 m², profit $50 - Product 2: time 3h, material A 3kg, material B 4kg, space 1.5 m², profit $70 - Product 3: time 1.5h, material A 4kg, material B 1kg, space 0.8 m², profit $40 - Product 4: time 4h, material A 6kg, material B 5kg, space 2 m², profit $90 - Product 5: time 2.5h, material A 2kg, material B 3kg, space 1.2 m², profit $60 Market constraints (maximum demand): - Product 1: 800 units - Product 2: 500 units - Product 3: 1000 units - Product 4: 300 units - Product 5: 600 units Additional conditions: - Product 4 can only be produced if Product 2 is produced - Minimum 100 units of Product 1 (base product) Maximize monthly profit. ``` ### Example 8: Scientific Research Planning ``` Help plan scientific research with MCP Optimizer. Research institute has: - Annual budget: $50 million - Research time: 10,000 person-hours - Laboratory equipment: 20 units Research projects: - Project A (medicine): budget $8M, time 1500h, equipment 3 units, scientific value 90 - Project B (energy): budget $12M, time 2000h, equipment 5 units, scientific value 95 - Project C (materials): budget $6M, time 1200h, equipment 2 units, scientific value 80 - Project D (AI): budget $10M, time 1800h, equipment 1 unit, scientific value 100 - Project E (ecology): budget $4M, time 800h, equipment 2 units, scientific value 70 - Project F (space): budget $15M, time 2500h, equipment 8 units, scientific value 98 - Project G (biotech): budget $7M, time 1300h, equipment 4 units, scientific value 85 - Project H (quantum): budget $20M, time 3000h, equipment 6 units, scientific value 100 Constraints: - Maximum 5 projects simultaneously - Project D requires completion of Project C - Minimum 1 project in medicine or biotechnology Maximize total scientific value of research. ``` ## Request Structure for MCP Optimizer ```python # Example for knapsack problem result = solve_knapsack_problem( items=[ {"name": "Item1", "weight": 10, "value": 60}, {"name": "Item2", "weight": 20, "value": 100}, {"name": "Item3", "weight": 30, "value": 120} ], capacity=50, knapsack_type="0-1" # or "bounded", "unbounded" ) ``` ## Typical Activation Phrases - "Solve a knapsack problem" - "Select optimal set of items" - "Maximize value with limited capacity" - "Optimize selection with limited budget" - "Find best combination of elements" - "Help with optimal selection" ## Applications Selection problems are used in: - Investment planning - Logistics and transportation - Resource management - Team formation - Production planning - Scientific research - Marketing and advertising