A company sells two products with information as follows: $$\begin{array} { | l | r | r | }
\hline & \mathrm { A } & \mathrm { B } \
\hline \text { Sales price per unit } & \$ 12.00 & \$ 28.00 \
\hline \text { Variable cost per unit } & \$ 10.00 & \$ 12.00 \
\hline
\end{array}$$ 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 3,000 machine hours available per month.The company can sell up to 18,000 units of product A per month,and up to 3,000 units of product B for the month.What is the optimum product mix to maximize company's operating income?

Question

A company sells two products with information as follows: $$\begin{array} { | l | r | r | } 
\hline & \mathrm { A } & \mathrm { B } \
\hline \text { Sales price per unit } & \$ 12.00 & \$ 28.00 \
\hline \text { Variable cost per unit } & \$ 10.00 & \$ 12.00 \
\hline
\end{array}$$ 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 3,000 machine hours available per month.The company can sell up to 18,000 units of product A per month,and up to 3,000 units of product B for the month.What is the optimum product mix to maximize company's operating income?

Quizplus · Accepted Answer

To find the optimum product mix, we need to use linear programming. Let x be the number of units of product A and y be the number of units of product B.

The objective function we want to maximize is the operating income, which is given by:
Operating Income = 18x + 20y

The constraints are:
4x + 2y ≤ 3,000 (machine hours)
x ≤ 18,000 (units of product A)
y ≤ 3,000 (units of product B)
x, y ≥ 0 (non-negativity)

Using a linear programming tool or method, we can find that the optimum solution is x = 6,000 and y = 3,000. Therefore, the best choice is B, which means the company should produce 6,000 units of product A and 3,000 units of product B to maximize its operating income.

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