Linear Programming Problem: Product Optimization
Problem Statement: A factory produces two types of products, A and B. Each product requires a certain amount of machine time and raw materials. The objective is to determine the optimal production quantity for each product to maximize the total profit.
Mathematical Formulation: Let:
x = Number of units of product A
y = Number of units of product B
Objective Function:
Maximize Profit = 3x + 4y
Constraints:
Machine Time Constraint:
2x + 3y ≤ 12
Raw Material Constraint:
x + 2y ≤ 8
Non-negativity Constraints:
x ≥ 0, y ≥ 0
Solution Approach: We will use the Python library PuLP to solve this linear programming problem.
Steps to Run the Code:
Install Required Libraries: Ensure you have PuLP installed. You can install it using pip:
Bash
pip install pulp
Use code with caution.
Write the Python Code: Create a Python script and implement the linear programming model using the PuLP library.
Run the Code: Execute the Python script to solve the LP problem and obtain the optimal solution.
Interpretation of Results: The optimal solution will provide the values of x and y that maximize the profit, given the constraints. This solution will help the factory make informed decisions about production quantities to achieve maximum profitability.