Maximising Profit with Resource Constraints?
A factory produces two products, A and B, using two resources, Labour and Machinery. Product A requires 3 units of Labour and 2 units of Machinery per unit produced, while Product B requires 2 units of Labour and 4 units of Machinery per unit produced. The factory has a maximum of 150 units of Labour and 200 units of Machinery available daily. Formulate a linear programming problem to maximise the total profit, which is ₹10 per unit of Product A and ₹15 per unit of Product B.
1 Answer
📌 CONCEPT: A linear programming problem is formulated to maximise the total profit by determining the optimal production levels of two products, subject to resource constraints.
📐 RULE / FORMULA: The objective function to be maximised is the total profit, which is ₹10 per unit of Product A and ₹15 per unit of Product B. The constraints are the resource availability, Labour (150 units) and Machinery (200 units), and the production requirements of each product.
💡 WORKED EXAMPLE: Let's consider the problem of maximising the profit from producing Product A and Product B. Suppose we let x be the number of units of Product A and y be the number of units of Product B. The objective function is 10x + 15y. The constraints are 3x + 2y ≤ 150 (Labour) and 2x + 4y ≤ 200 (Machinery).
⚠️ COMMON MISTAKE: One common mistake students make is not considering all possible constraints and objective functions, leading to an incorrect or incomplete solution.
30 Aug 26
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