Consider the following production and cost data for two products,L and C:

$\begin{array}{l r r}
& \underline { \text { Product L } } & \underline { \text { Product C } } \
\text { Contribution Margin per Unit }& \$ 130 & \$ 120 \
\text { Machine Setups Needed per Unit } &10\text { setups }&8 \text { setups }
\end{array}$

The company can only perform 65,000 machine setups each period due to limited skilled labour,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) $910,000.
C) $975,000.
D) $1,820,000.

Question

Consider the following production and cost data for two products,L and C:

$\begin{array}{l r r}
 & \underline { \text { Product L } } & \underline { \text { Product C } } \
\text { Contribution Margin per Unit }& \$ 130 & \$ 120 \
\text { Machine Setups Needed per Unit } &10\text { setups }&8 \text { setups }
\end{array}$

The company can only perform 65,000 machine setups each period due to limited skilled labour,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) $910,000.
C) $975,000.
D) $1,820,000.

Quizplus · Accepted Answer

To maximize the total contribution margin, we need to determine the optimal production quantity for each product based on the limited machine setups.

Let L be the number of units of product L produced and C be the number of units of product C produced. Then, we have:

10L + 8C ≤ 65,000   (due to limited machine setups)

To maximize the total contribution margin, we need to produce the product that has a higher contribution margin per unit. In this case, it is product L with a contribution margin of $130 per unit. Therefore, we should produce as many units of product L as possible subject to the constraint above.

Let's solve for L:

10L + 8C ≤ 65,000
10L ≤ 65,000 - 8C
L ≤ 6,500 - 0.8C

To maximize L, we want to set C to be as small as possible, which is 0. Therefore:

L ≤ 6,500

Now let's calculate the total contribution margin:

Total contribution margin = (contribution margin per unit) x (number of units produced)
= (130) x (6,500)
= $845,000

Therefore, the largest possible total contribution margin that can be realized each period is $845,000. The answer is (C).

Consider the Following Production and Cost Data for Two Products,L