Example: Cost Minimization for a Manufacturing Company Imagine a company that produces two products, Product A and Product B. To minimize costs, they need to decide how much of each product to manufacture while adhering to various constraints. Let's represent the number of units of Product A as X and the number of units of Product B as Y. The company's goal is to minimize their production costs while meeting demand and resource limitations. Constraints: Limited Resources: The company has a limited supply of raw materials, and each unit of Product A requires 3 units of raw material A, while each unit of Product B requires 2 units of raw material A and 1 unit of raw material B. The total supply of raw materials A and B is limited to 300 and 150 units, respectively. This constraint can be expressed as: 3X + 2Y 300 (Raw material A constraint) Y 150 (Raw material B constraint) Demand: The company needs to meet the market demand for each product, with a minimum requirement of 100 units of Product A and 50 units of Product B: X 100 (Demand for Product A) Y 50 (Demand for Product B)