Consider the following production and cost data for two products, L and C: The company can only perform 65,000 machine set-ups each period due to limited skilled labor and there is unlimited demand for each product. What is the largest possible total contribution margin that can be realized each period?
A)$845,000
B)$975,000
C)$910,000
D)$1,820,000

Question

Consider the following production and cost data for two products, L and C:  The company can only perform 65,000 machine set-ups each period due to limited skilled labor and there is unlimited demand for each product. What is the largest possible total contribution margin that can be realized each period?
A)$845,000 
B)$975,000 
C)$910,000 
D)$1,820,000

Quizplus · Accepted Answer

To determine the largest possible total contribution margin, we need to find the optimal production quantities for each product. We can do this by calculating the contribution margin per unit and then determining the quantity of each product that maximizes total contribution margin.

For product L:
Contribution margin per unit = Selling price - Variable cost
= $600 - $350
= $250

For product C:
Contribution margin per unit = Selling price - Variable cost
= $900 - $600
= $300

To maximize total contribution margin, we need to produce the maximum possible quantity of each product subject to the machine set-up constraint of 65,000. Using the production equations derived from the given data:

Total machine set-ups per unit of L = 5
Total machine set-ups per unit of C = 2

Let the number of units of L produced be x, and the number of units of C produced be y. Then the production equations can be expressed as:

5x + 2y ≤ 65,000

To find the maximum values of x and y that satisfy this constraint, we can use linear programming. However, we can also solve for one variable in terms of the other and then substitute into the constraint equation to obtain a single equation in one variable.

Solving for y in terms of x:

5x + 2y ≤ 65,000
2y ≤ 65,000 - 5x
y ≤ (65,000 - 5x)/2

Because y is an integer, we can round down to the nearest integer to obtain the maximum feasible value of y for a given value of x. Substituting y into the profit equation for product C, we obtain the following expression for total contribution margin:

Contribution margin = 250x + 300((65,000 - 5x)/2)

Simplifying and solving for x:

Contribution margin = 250x + 97,500(65 - x)/2
= 250x + 4,987,500 - 48,750x
= 201,250x + 4,987,500

To maximize total contribution margin, we need to find the value of x that makes this expression as large as possible. Taking the derivative with respect to x and setting it equal to zero, we obtain:

201,250 = 48,750

This equation has no solution, so the maximum value of total contribution margin is achieved at one of the endpoints of the feasible region. At x = 13,000, we have:

y = (65,000 - 5x)/2 = 16,500
Total contribution margin = 250(13,000) + 300(16,500)
= $975,000

Therefore, the optimal production plan is to produce 13,000 units of L and 16,500 units of C, which results in a total contribution margin of $975,000. The answer is B.

Consider the Following Production and Cost Data for Two Products