Edison Company produces two types of piano legs, plain and fancy, which have unit contribution margins of $8 and $12, respectively. Each piano leg must spend time on a special machine. The firm owns four machines that together provide 10,000 hours of machine time per year. The plain leg requires 0.25 hours of machine time, and the fancy leg requires 0.5 hours of machine time.
-Refer to the Figure.What is the total contribution margin of the optimal mix of plain and fancy legs?
A)$240,000
B)$280,000
C)$320,000
D)$480,000

Question

Quizplus · Accepted Answer

To find the optimal mix, we can use linear programming.

Let x be the number of plain legs and y be the number of fancy legs.

The objective function is:

Maximize 8x + 12y

Subject to the constraints:

0.25x + 0.5y ≤ 10,000 (machine time constraint)

x, y ≥ 0 (non-negativity constraint)

Solving this linear program, we get x = 20,000 and y = 10,000.

Plugging these values into the objective function, we get:

Total contribution margin = 8(20,000) + 12(10,000) = $320,000

Therefore, the total contribution margin of the optimal mix of plain and fancy legs is $320,000.

The best choice is to produce 20,000 plain legs and 10,000 fancy legs to maximize the contribution margin.

Edison Company Produces Two Types of Piano Legs, Plain and Fancy