Question

Determining the Optimal Product Mix with One Constrained Resource and a Sales Constraint

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 50,220 units of each sweatshirt can be sold.

Required:

If required, round your answers to the nearest whole number.

1. What is the contribution margin per hour of machine time for each type of sweatshirt?

	Contribution Margin
Swoop	$
Rufus	$

2. What is the optimal mix of sweatshirt?

	Optimal Mix
Swoop	units
Rufus	units

3. What is the total contribution margin earned for the optimal mix?
$

Answer 1

1.Calculation of contribution margin per machine hour

	Swoop	Rufus
Contribution Margin per Unit (A)	5	15
Hours per Unit (B)	0.1	0.5
Contribution margin per hour (A/B)	50	30

2.Optimal mix

Since the contribution margin per machine hour is higher for Swoop, the priority will be given to Swoop and the remaining hours will be used for the production of Rufus

Product	Units	Machine hours per unit	Total Machine Hours
Swoop	50,220	0.1	5,022
Rufus	3,956	0.5	1,978
		Total	7,000

3.Total contribution margin = 50,220*5 + 3,956*15

= $310,440