Question

Determining the Optimal Product Mix with One Constrained Resource

Comfy Fit Company manufactures two types of university sweatshirts, the Swoop and the Rufus, with unit contribution margins of $8 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 there are no other constraints.

Required:

If required, round your answers to the nearest whole number. If an amount is zero, enter "0".

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.
	Swoop	Rufus
Contribution margin per unit	8	15
Required time per unit	0.10	0.50
	(6/60)	(6/30)
Contribution margin per hour of machine time	80	30
	(8/0.10)	(15/0.50)
2
Since the contribution margin per hour of machine time for Swoop is higher than Rufus
Company should use all the machine hour to product Swoop
No of Swoop units = 1000/0.10	10000
The optimal mix of sweatshirt would be
Swoop	10,000	units
Rufus	0
3
The total contribution margin earned by company would be (10,000*8) = $ 80,000