Question

PPL Ltd. produces two types of products, A and B, using 10 machines, 1 and 2 . Machine 1 produces one unit of product A in 4 hours, while machine 2 takes 2 hours to produce one of unit of product A. On the other hand, machine 1 produces one unit of product B in 2 hours, whereas machine 2 takes 6 hours to produce one unit of product B. The revenues generated from products A and B are 60 and 40 , respectively. The total processing time for both the machines is 16 hours daily. Determine how many units of products A and B the organization should produce on a daily basis to maximize profits. Use graphical Method.

Answer 1

To maximize profits, the organization should produce a certain number of product A and product B daily by graphing the constraints and evaluating the objective function at the corner points of the feasible region.

Step-by-step explanation:

To determine how many units of products A and B the organization should produce daily to maximize profits, we can use the graphical method of linear programming. Let's assume that the organization produces x units of product A and y units of product B.

Objective function: Maximize profit = 60x + 40y

Constraints:

• Machine 1 time constraint: 4x + 2y ≤ 16
• Machine 2 time constraint: 2x + 6y ≤ 16
• Non-negativity constraint: x ≥ 0, y ≥ 0

We can plot these constraints on a graph and find the feasible region. Then, we can evaluate the objective function at the corner points of the feasible region to find the maximum profit.