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 $4 on each unit of product A and $4 on each unit of product B. To manufacture a unit of product A requires 5 min on machine I and 4 min on machine II. To manufacture a unit of product B requires 9 min on machine I and 5 min on machine II. There are 100 min available on machine I and 80 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?

Machine 1: 11 units of A and 5 units of B should be produced.

Machine II: 15 units of A and 4 units of B should be produced.

Explanation:

To maximize the company's profit, the products that requires lesser time to produce should be produced in more quantity since the profit of both products are the same.

Machine 1:

Available time = 100 min

Each unit of A requires 5 min to produce

11 units of A would require = 11*5 = 55 units

Each unit of B requires 9 min to produce

5 units of B would require 5*9 = 45 min

Total time taken = 55 min + 45 min = 100 min = available time

Machine II:

Available time = 80 min

Each unit of A requires 4 min to produce

15 units of A would require 15*4 = 60 min

Each unit of B requires 5 min to produce

4 units of B would require = 5*4 = 20 min

Total time taken = 60 min + 20 min = 80 min = available time