Figure 13-4. Connolly Company produces two types of lamps,classic and fancy,with unit contribution margins of $13 and $21,respectively.Each lamp must spend time on a special machine.The firm owns four machines that together provide 18,000 hours of machine time per year.The classic lamp requires 0.20 hours of machine time,the fancy lamp requires 0.50 hours of machine time.
Refer to Figure 13-4.What is the total contribution margin of the optimal mix of classic and fancy lamps?
A)$1,280,000
B)$950,000
C)$1,000,000
D)$1,170,000
E)$90,000

Question

Quizplus · Accepted Answer

To find the optimal mix, we need to use the concept of linear programming. Let x be the number of units of the classic lamp and y be the number of units of the fancy lamp produced.
The objective function is:
Contribution Margin = 13x + 21y
The constraints are:
0.20x + 0.50y ≤ 18,000 (machine time constraint)
x ≥ 0 and y ≥ 0 (non-negativity constraint)
Solving the above equations, we get:
x = 54,000 and y = 24,000
Total Contribution Margin = 13x + 21y = $1,170,000
Therefore, the best choice is D.