Maximizing Profit: A Constrained Problem?
The XYZ Corporation produces two products, A and B, which require 3 hours and 2 hours of labor respectively. The profit per unit of A is ₹ 100 and B is ₹ 150. If the available labor is limited to 120 hours and 50 units of product A and 30 units of product B are already in production, formulate and solve the linear programming problem to maximize the total profit.
1 Answer
📌 CONCEPT: Linear Programming is a method used to find the optimal solution to a problem that involves maximizing or minimizing a linear objective function, subject to a set of linear constraints.
📐 RULE / FORMULA: The objective function is maximized or minimized by finding the optimal values of the decision variables that satisfy the constraints.
💡 WORKED EXAMPLE: Suppose we have a problem where we want to maximize profit by producing two products A and B. Let x be the number of units of product A produced and y be the number of units of product B produced. The objective function is Maximize 100x + 150y. The constraints are 3x + 2y ≤ 120 (labor constraint), x ≤ 50 (existing production of A), and y ≤ 30 (existing production of B). To solve this problem, we need to find the values of x and y that maximize the objective function and satisfy the constraints.
⚠️ COMMON MISTAKE: Students often forget to consider all the constraints in the problem and may end up with an infeasible solution.
10 Sept 26
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