A company sells two products with information as follows: $$\begin{array} { | l | r | r |}
\hline & \mathrm { A } & \mathrm { B } \
\hline \text { Sales price per unit } & \$ 11.00 & \$ 20.00 \
\hline \text { Variable cost per unit } & \$ 10.00 & \$ 10.00 \
\hline
\end{array}$$ 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 3000 machine hours available per month. The company can sell up to 18,000 units of product A per month, and up to 3000 units of product B for the month. What is the optimum product mix to maximize the company's operating income?

Question

A company sells two products with information as follows: $$\begin{array} { | l | r | r |} 
\hline & \mathrm { A } & \mathrm { B } \
\hline \text { Sales price per unit } & \$ 11.00 & \$ 20.00 \
\hline \text { Variable cost per unit } & \$ 10.00 & \$ 10.00 \
\hline
\end{array}$$ 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 3000 machine hours available per month. The company can sell up to 18,000 units of product A per month, and up to 3000 units of product B for the month. What is the optimum product mix to maximize the company's operating income?

Quizplus · Accepted Answer

To maximize operating income, calculate the contribution margin per machine hour for each product. Product A: $(11 - 10) 	imes 4 = $4 per machine hour. Product B: $(20 - 10) 	imes 2 = $20 per machine hour. Given the machine hour limit and demand, the mix that maximizes income within constraints is 6000 units of A (using 1500 machine hours) and 3000 units of B (using 1500 machine hours), totaling 3000 machine hours.

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