A company sells two products with information as follows: $$\begin{array} { | l | r | r| }
\hline & \mathrm { A } & \mathrm { B } \
\hline \text { Sales price per unit } & \$ 11.00 & \$ 20.00 \
\hline \text { Variable cost per unit } & \$ 10.00 & \$ 12.00 \
\hline
\end{array}$$ The products are machine made. Four units of product A can be made with one machine hour, and two units of product B can be made with one machine hour. The company has a maximum of 3000 machine hours available per month. The company can sell up to 17,000 units of product A per month and up to 3000 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: $$\begin{array} { | l | r | r| } 
\hline & \mathrm { A } & \mathrm { B } \
\hline \text { Sales price per unit } & \$ 11.00 & \$ 20.00 \
\hline \text { Variable cost per unit } & \$ 10.00 & \$ 12.00 \
\hline
\end{array}$$ The products are machine made. Four units of product A can be made with one machine hour, and two units of product B can be made with one machine hour. The company has a maximum of 3000 machine hours available per month. The company can sell up to 17,000 units of product A per month and up to 3000 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 contribution margin per unit for product A is $1 ($11 - $10), and for product B is $8 ($20 - $12). With 3000 machine hours, the company can produce 12,000 units of A (4 units/hour) or 6,000 units of B (2 units/hour). However, due to sales constraints, they can only sell 17,000 units of A and 3,000 units of B. The optimal strategy is to produce and sell 3,000 units of B (using 1,500 hours) and use the remaining 1,500 hours to produce 6,000 units of A. The total contribution margin is (3,000 units of B * $8) + (6,000 units of A * $1) = $24,000 + $6,000 = $30,000.

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