Question

Comfy Fit Company manufactures two types of university sweatshirts, the Swoop and the Rufus, with unit contribution margins of $5 and $15, respectively. Regardless of type, each sweatshirt must be fed through a stitching machine to affix the appropriate university logo. The firm leases seven machines that each provides 1,000 hours of machine time per year. Each Swoop sweatshirt requires 6 minutes of machine time, and each Rufus sweatshirt requires 30 minutes of machine time.

Assume that a maximum of 40,000 units of each sweatshirt can be sold.

Required:
a. What is the contribution margin per hour of machine time for the Swoop sweatshirts?
b. What is the contribution margin per hour of machine time for the Rufus sweatshirts?
c. What is the optimal mix of sweatshirts?
d. What is the total contribution margin earned for the optimal mix?

Answer 1

Comfy Fit Company

a. The contribution margin per hour of machine time for the Swoop is:

= $50.

b. The contribution margin per hour of machine time for the Rufus sweatshirts is:

= $30.

c. The optimal mix of sweatshirts that maximizes profitability is 40,000 Swoop sweatshirts and 6,000 Rufus sweatshirts.

d. The total contribution margin earned for the optimal mix is:

= $2,180,000.

Step-by-step explanation:

a) Data and Calculations:

Machine hours available = 7,000 hours (1,000 * 7)

Swoop Rufus

Contribution margins $5 $15

Time required per unit 6 min 30 min

Time required per unit in hours 0.10 hr 0.5 hrs

Contribution per hour $50 $30

Optimal product mix is to produce all of Swoop's 40,000 units first and then to use the remaining machine hours (3,000) to produce Rufus sweatshirts.

This will take 4,000 hours (40,000 * 0.10)

This leaves 3,000 hours for Rufus (7,000 - 4,000)

This means that only 6,000 (3,000/0.5) of Rufus can be produced

The total contribution margin for the optimal mix:

= ($50 * 40,000) + ($30 * 6,000)

= $2,000,000 + 180,000

= $2,180,000