Question

Formulate but do not solve the following exercise as a linear programming problem.A company manufactures x units of product A and y units of product B, on two machines, I and II. It has been determined that the company will realize a profit of $2 on each unit of product A and $4 on each unit of product B. To manufacture a unit of product A requires 7 min on machine I and 3 min on machine II. To manufacture a unit of product B requires 9 min on machine I and 3 min on machine II. There are 154 min available on machine I and 66 min available on machine II in each work shift. How many units of a product should be produced in each shift to maximize the company's profit P?P =______ subject to the constraints.machine I ______.machine II _______.x = 0 ________.y = 0 _________.

Answer 1

Answer: Maximize the Objective Function

2x + 4y = z

Subject to:

Machine L 7x + 9y ≤ 154

Machine LL 3x + 3y ≤ 66

Explanation:

From problem statement :

Let :

x units of product A per shift

y units of product B per shift

Profit on each A unit 2$

Profit on each B unit 4$

Product A needed time in machine L 7 min and 3 min in machine LL

Poduct B needed time in machine L 9 min and 3 min in machine LL

Available time 154 min machine L 66 min machine LL (by shift )

Then: Objective function to maximize z

z = 2x + 4y

Constraints

Machine L 7x + 9y ≤ 154

Machine LL 3x + 3y ≤ 66