Question

A company manufactures x units of Product A and y units of Product 8, on two machines, I and II. It has been determined that the company will realize a profit of unit of Product A and a profit of $4/unit of Product B. To manufacture a unit of Product A requires 6 min on Machine 1 and 5 min on Machine Il. To manufacture a unit of Product requires 9 min on Machine and 4 min on Machine IL There are 5 hr of machine time available on Machine 1 and 3 hr of machine time available on Machine II in each work . How many units of each product should be produced in each shift to maximize the company's profit? xn-( What is the optimal profit? (Round your answer to the nearest whole number) Need Help?

Answer 1

Answers:

(x, y) = (50, 45)

Optimal profit = $330

Thus 50 units of A and 45 units of B will be manufactured and maximized profit will be $330.

Explanation:

I have solved the above in excel using the solver function. The variables have been defined as below:

	Machine I	Machine II
Product A	a1	a2
Product B	b1	b2

Profit = (a1+a2)*$3 + (b1+b2)*$4

Constraints:

(i): a1 + b1 <= 300 (i.e. 5 hours = 300 minutes). This is Machine I's time constraint

(ii) a2 + b2<= 180 (i.e. 3 hours = 180 minutes). This is Machine II's time constraint.

Solving using excel's solver we get the following result:

	Machine I	Machine II
Product A	50.00	-
Product B	-	45.00
Profit of A	150.00
Profit of B	180.00
Total profit	330.00
Constraints
300.00	<=	300.00	Machine I time constraint in minutes
180.00	<=	180.00	Machine II time constraint in minutes