A company sells two products with information as follows: $$\begin{array} { | l | r | r | }
\hline & { \text { A } } & { \text { B } } \
\hline \text { Price per unit } & \$ 12 & \$ 20 \
\hline \text { Variable cost per unit } & \$ 10 & \$ 12 \
\hline
\end{array}$$ Products are made by machine. 4 units of Product A can be made with one machine hour and 2 units of Product B can be made with one machine hour. The company has a maximum of 3,000 machine hours available per month. The company can sell up to 7,000 units of Product A per month, and up to 3,000 units of Product B for the month. What is the maximum amount of contribution margin that the company could earn in a month given the stated constraints?

Question

A company sells two products with information as follows: $$\begin{array} { | l | r | r | } 
\hline &  { \text { A } } & { \text { B } } \
\hline \text { Price per unit } & \$ 12 & \$ 20 \
\hline \text { Variable cost per unit } & \$ 10 & \$ 12 \
\hline
\end{array}$$ Products are made by machine. 4 units of Product A can be made with one machine hour and 2 units of Product B can be made with one machine hour. The company has a maximum of 3,000 machine hours available per month. The company can sell up to 7,000 units of Product A per month, and up to 3,000 units of Product B for the month. What is the maximum amount of contribution margin that the company could earn in a month given the stated constraints?

Quizplus · Accepted Answer

The maximum contribution margin is earned when the company produces and sells the maximum number of units of the product with the higher contribution margin per unit. In this case, Product B has a higher contribution margin per unit ($20 - $12 = $8) than Product A ($12 - $10 = $2). Therefore, the company should produce and sell as many units of Product B as possible, up to the maximum demand of 3,000 units.To determine the maximum number of units of Product A that can be produced, we need to consider the machine hour constraint. Since 2 units of Product B can be made with one machine hour, the company can produce a maximum of 3,000 machine hours / 2 units per machine hour = 1,500 units of Product B.Since 4 units of Product A can be made with one machine hour, the company can produce a maximum of 3,000 machine hours / 4 units per machine hour = 750 units of Product A.Therefore, the company can produce and sell a maximum of 1,500 units of Product B and 750 units of Product A.The maximum contribution margin is:1,500 units of Product B x $8 contribution margin per unit = $12,000750 units of Product A x $2 contribution margin per unit = $1,500Total maximum contribution margin = $12,000 + $1,500 = $13,500

A Company Sells Two Products with Information as Follows Products Are Made by Machine