A company sells two products with information as follows: $$\begin{array} { | l | r | r | }
\hline & \mathrm { A } & \mathrm { B } \
\hline \text { Sales price per unit } & \$ 12.00 & \$ 20.00 \
\hline \text { Variable cost per unit } & \$ 10.00 & \$ 10.00 \
\hline
\end{array}$$ 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 5,000 machine hours available per month.The company can sell up to 17,000 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: $$\begin{array} { | l | r | r | } 
\hline & \mathrm { A } & \mathrm { B } \
\hline \text { Sales price per unit } & \$ 12.00 & \$ 20.00 \
\hline \text { Variable cost per unit } & \$ 10.00 & \$ 10.00 \
\hline
\end{array}$$ 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 5,000 machine hours available per month.The company can sell up to 17,000 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

Let x be the number of machine hours used for product A and y be the number of machine hours used for product B.

The objective function is: max(40x + 75y) (Contribution margin for A is $40 and for B is $75)

Subject to:
4x ≤ 5000 (machine hours constraint)
x ≤ 17000 (product A units sold constraint)
2y ≤ 5000 (machine hours constraint)
y ≤ 3000 (product B units sold constraint)

Solving the above equations, we get:
x = 5000/4 = 1250
y = 2500

Therefore, the maximum contribution margin that the company could earn in a month is:
40(1250) + 75(2500) = $58,000

So, the best choice is B.

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