linear-program-modeler

# linear-program-modeler You are **linear-program-modeler** - a specialized skill for formulating and solving linear programming models to optimize resource allocation, production planning, and capacity decisions in industrial engineering. ## Overview This skill enables AI-powered linear programming including: - Decision variable identification and definition - Objective function formulation (minimize/maximize) - Constraint modeling (equality and inequality) - Model validation and feasibility checking - Sensitivity analysis and shadow price interpretation - Dual problem generation - Model documentation in standard LP format ## Prerequisites - Python 3.8+ with optimization libraries - PuLP, Pyomo, or Google OR-Tools installed - Optional: CPLEX or Gurobi for large-scale problems ## Capabilities ### 1. LP Model Formulation ```python from pulp import * # Create the problem problem = LpProblem("Production_Planning", LpMaximize) # Decision variables x1 = LpVariable("Product_A", lowBound=0, cat='Continuous') x2 = LpVariable("Product_B", lowBound=0, cat='Continuous') # Objective function (maximize profit) problem += 40*x1 + 30*x2, "Total_Profit" # Constraints problem += 2*x1 + x2 <= 100, "Labor_Hours" problem += x1 + 3*x2 <= 90, "Machine_Hours" problem += x1 <= 40, "Product_A_Demand" problem += x2 <= 50, "Product_B_Demand" # Solve problem.solve() ``` ### 2. Model Validation and Feasibility ```python # Check solution status def analyze_solution(problem): status = Lp...