A company produces product A and product B.Each product must go through two processes.Each A produced requires two hours in process 1 and five hours in process 2.Each B produced requires six hours in process 1 and three hours in process 2.There are 80 hours of capacity available each week in each process.Each A produced generates $6.00 in profit for the company.Each B produced generates $9.00 in profit for the company.If the company produces 6 units of A and 9 units of B the value of the objective function is equal to
A)$36.
B)$81.
C)$108.
D)$117

Question

Quizplus · Accepted Answer

To maximize the profit, we need to formulate the problem as a linear programming problem. Let x be the number of units of product A and y be the number of units of product B.

The objective function to be maximized is:

Profit = 6x + 9y

Subject to the following constraints:

2x + 6y ≤ 80 (process 1 constraint) 
5x + 3y ≤ 80 (process 2 constraint)

Also, x ≥ 0 and y ≥ 0

Solving these equations, we get x = 6 and y = 9.

Therefore, the value of the objective function is:

Profit = 6x + 9y = 6(6) + 9(9) = $117

Thus, the best choice is D.

A Company Produces Product a and Product B