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()

# Check solution status
def analyze_solution(problem):
    status = LpStatus[problem.status]

    if status == "Optimal":
        print(f"Optimal value: {value(problem.objective)}")
        for v in problem.variables():
            print(f"{v.name} = {v.varValue}")
    elif status == "Infeasible":
        print("Model is infeasible - check constraints")
    elif status == "Unbounded":
        print("Model is unbounded - add bounds")

    return status

# Shadow prices and reduced costs
def sensitivity_analysis(problem):
    results = {
        "shadow_prices": {},
        "reduced_costs": {},
        "binding_constraints": []
    }

    for name, constraint in problem.constraints.items():
        shadow_price = constraint.pi
        slack = constraint.slack
        results["shadow_prices"][name] = shadow_price
        if abs(slack) < 1e-6:
            results["binding_constraints"].append(name)

    for v in problem.variables():
        results["reduced_costs"][v.name] = v.dj

    return results

Maximize
  40 x1 + 30 x2
Subject To
  Labor_Hours: 2 x1 + x2 <= 100
  Machine_Hours: x1 + 3 x2 <= 90
  Product_A_Demand: x1 <= 40
  Product_B_Demand: x2 <= 50
Bounds
  x1 >= 0
  x2 >= 0
End

{
  "model_name": "Production_Planning",
  "sense": "maximize",
  "status": "optimal",
  "objective_value": 1600.0,
  "decision_variables": {
    "Product_A": 30.0,
    "Product_B": 20.0
  },
  "sensitivity": {
    "shadow_prices": {
      "Labor_Hours": 15.0,
      "Machine_Hours": 5.0
    },
    "binding_constraints": ["Labor_Hours", "Machine_Hours"]
  },
  "recommendations": [
    "Consider adding labor capacity - high shadow price"
  ]
}