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. Assume there are no constraints on sales of either product, and the company could choose any product mix they wish. What is the maximum amount of contribution margin that the company could earn in a month?

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. Assume there are no constraints on sales of either product, and the company could choose any product mix they wish. What is the maximum amount of contribution margin that the company could earn in a month?

Quizplus · Accepted Answer

Let's represent the number of machine hours used to make Product A as x and the number of machine hours used to make Product B as y. We want to maximize the contribution margin which is revenue minus variable costs.

Let's first find the contribution margin per unit of each product:
- Product A: $140 - $100 = $40
- Product B: $190 - $140 = $50

Now we can write out the objective function for the problem:
Maximize: 40x + 50y (contribution margin)
Subject to:
4x + 2y ≤ 3000 (machine hours constraint)

Solving the inequality for y in terms of x, we get:
y ≤ -2x + 1500

We can graph this inequality to see the feasible region:

```
^
|     /
|   /
| /
|_________
0       x
```
The feasible region is the shaded area below the line y = -2x + 1500. The vertices of the feasible region are (0, 750), (500, 1000), and (750, 0). We can evaluate the objective function at each vertex to see which one gives the maximum contribution margin:

- (0, 750): 40(0) + 50(750) = $37,500
- (500, 1000): 40(500) + 50(1000) = $65,000
- (750, 0): 40(750) + 50(0) = $30,000

Therefore, the maximum contribution margin the company could earn in a month is $65,000, which corresponds to producing and selling 500 units of Product A and 1000 units of Product B. Answer choice C is correct.

A Company Sells Two Products with Information as Follows