Question

etermining 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 $11 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)contribution per hour =contribution per unit *60 minutes /time per unit

		contribution per hour
Swoop	11*60/6	$ 110 per hour
Rufus	15*60/30	$ 30 per hour

2)since contribution per hour of Swoop is higher than Rufus therefore all of the units Swoop should be manufactured in available time

Hours available =1000*7= 7000

Therefore optimal mix:

		number of units
Swoop	7000*60/6	70000
Rufus	7000-7000	0

3)Total contribution per earned = units produced* contribuion per unit

          =[70000*11]+[0*15)

         = 770000+0

            = $ 770000