Southern Production Company has 100 labor-hours available. There is no limit on machine-hours. Southern can sell all of B it wants, but it can only sell 45 units and 20 units of A and C, respectively.
Product A Product B Product C
Contribution margin per unit $15 $10 $12
Labor-hours per unit 2.5 2.5 2
Machine-hours per unit 5 3.5 1
a) What is the contribution margin per labor-hour for Product A?
b) What is the contribution margin per labor-hour for Product B?
c) What is the contribution margin per labor-hour for Product C?
d) How many units of Product A should the company make?
e) How many units of Product B should the company make?
f) How many units of Product C should the company make?
6,000
To answer these questions, we need to calculate the contribution margin per labor-hour for each product. The formula for contribution margin per labor-hour is:
Contribution margin per labor-hour = Contribution margin per unit / Labor-hours per unit
Given the information provided, we can calculate the contribution margin per labor-hour for each product:
a) For Product A:
Contribution margin per labor-hour = $15 / 2.5 labor-hours per unit = $6 per labor-hour
b) For Product B:
Contribution margin per labor-hour = $10 / 2.5 labor-hours per unit = $4 per labor-hour
c) For Product C:
Contribution margin per labor-hour = $12 / 2 labor-hours per unit = $6 per labor-hour
Now, let's calculate the number of units of each product the company should make.
d) For Product A:
The company can sell 45 units of Product A. Since each unit requires 2.5 labor-hours, the total number of labor-hours required for 45 units would be:
45 units * 2.5 labor-hours per unit = 112.5 labor-hours
e) For Product B:
The company can sell as many units of Product B as it wants. Since each unit requires 2.5 labor-hours, the company should maximize its profit by producing as many units as possible within the available 100 labor-hours.
f) For Product C:
The company can sell 20 units of Product C. Since each unit requires 2 labor-hours, the total number of labor-hours required for 20 units would be:
20 units * 2 labor-hours per unit = 40 labor-hours
Therefore, to summarize:
a) The contribution margin per labor-hour for Product A is $6.
b) The contribution margin per labor-hour for Product B is $4.
c) The contribution margin per labor-hour for Product C is $6.
d) The company should make 45 units of Product A.
e) The company should produce as many units of Product B as possible within the available 100 labor-hours.
f) The company should make 20 units of Product C.