A company sells two products with information as follows: Products are made by machine. 4 units of Product A can be made with one machine hour and 2 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 7,000 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:  Products are made by machine. 4 units of Product A can be made with one machine hour and 2 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 7,000 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 maximize operating income, we need to determine the contribution margin per unit for each product. 
For Product A: 
Selling price - variable cost = contribution margin 
Let x = selling price of Product A 
x - (4/1) = x - 4 = contribution margin 
For Product B: 
Selling price - variable cost = contribution margin 
Let y = selling price of Product B 
y - (2/1) = y - 2 = contribution margin

Next, we can set up the following linear programming problem: 
Maximize: (x - 4)A + (y - 2)B 
subject to: 
4A + 2B <= 3000 (machine hours constraint) 
A <= 7000 (Product A sales constraint) 
B <= 3000 (Product B sales constraint)

Using a linear programming solver or graphing the constraints, we find that the optimal solution is to produce 6,000 units of Product A and 3,000 units of Product B. Therefore, the answer is B.

A Company Sells Two Products with Information as Follows