A company sells two products with information as follows: $$\begin{array} { | l | c | c | }
\hline & \mathrm { A } & \mathrm { B } \
\hline \text { Sales price per unit } & \$ 11.00 & \$ 26.00 \
\hline \text { Variable cost per unit } & \$ 10.00 & \$ 10.00 \
\hline
\end{array}$$ 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 4000 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: $$\begin{array} { | l | c | c | } 
\hline & \mathrm { A } & \mathrm { B } \
\hline \text { Sales price per unit } & \$ 11.00 & \$ 26.00 \
\hline \text { Variable cost per unit } & \$ 10.00 & \$ 10.00 \
\hline
\end{array}$$ 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 4000 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 $16 ($26 - $10). Given the machine hour constraints, the maximum units of A that can be produced are 16,000 (4,000 machine hours * 4 units/hour) and of B are 8,000 (4,000 machine hours * 2 units/hour). However, the sales limit for A is 17,000 units and for B is 3,000 units. Therefore, the maximum units that can be sold given the constraints are 16,000 of A and 3,000 of B. The total contribution margin is (16,000 units of A * $1) + (3,000 units of B * $16) = $16,000 + $48,000 = $64,000. However, due to an oversight in calculation, the correct approach to maximize contribution margin would prioritize product B due to its higher contribution margin per unit and per machine hour. Let's correct the approach:Given the constraints and aiming to maximize contribution margin, we should prioritize product B due to its higher contribution margin per unit and per machine hour. 1. For product B, the maximum units that can be sold are 3,000, which requires 1,500 machine hours (3,000 units / 2 units per hour).2. This leaves 2,500 machine hours for product A (4,000 total machine hours - 1,500 used for B), which can produce 10,000 units of A (2,500 machine hours * 4 units per hour).The contribution margin for these units would be:- For A: 10,000 units * $1 = $10,000- For B: 3,000 units * $16 = $48,000Total contribution margin = $10,000 (from A) + $48,000 (from B) = $58,000.Therefore, the maximum amount of contribution margin the company could earn in a month, given the stated constraints, is $58,000.

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