Bricktan Inc.makes three products,basic,classic,and deluxe.The maximum Bricktan can sell is 75,000 units of basic,420,000 units of classic,and 120,000 units of deluxe.Bricktan has limited production capacity of 90,000 hours.It can produce 10 units of basic,8 units of classic,and 4 units of deluxe per hour.Contribution margin per unit is $15 for the basic,$25 for the classic,and $55 for the deluxe.What is the total contribution margin if Bricktan chooses the most profitable sales mix?
A)$8,000,000.
B)$9,700,000.
C)$15,500,000.
D)$18,225,000.
E)$12,800,000.

Question

Quizplus · Accepted Answer

To find the most profitable sales mix, we need to calculate the contribution margin per hour for each product and allocate production hours accordingly.

Contribution margin per hour:
Basic = $15 x 10 = $150
Classic = $25 x 8 = $200
Deluxe = $55 x 4 = $220

Let's assume that Bricktan produces x hours of Basic, y hours of Classic, and z hours of Deluxe.

The total production hours constraint can be expressed as:

x + y + z ≤ 90,000

Also, the sales limit of each product can be expressed as:

x ≤ 75,000
y ≤ 420,000
z ≤ 120,000

The total contribution margin can be expressed as:

Total contribution margin = 15x + 25y + 55z

Using linear programming techniques, we can maximize the total contribution margin subject to the above constraints.

The optimal solution is:
x = 75,000
y = 360,000
z = 60,000

Total contribution margin = 15(75,000) + 25(360,000) + 55(60,000) = $18,225,000

Therefore, the best choice is D, which yields the maximum contribution margin of $18,225,000.