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 51,260 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

Part-1
	Contribution Margin per Hour
Swoop	$50.00
Rufus	$30.00

Part-2
	Optimal Mix
Swoop	51260 unitt
Rufus	3748 Unit

Part-3 Computation of Total Contribution margin
	Contribution Margin per Unit	Optimal Mix	Total Contribution margin
Swoop	$5.00	51260	$256,300.00
Rufus	$15.00	3748	$56,220.00
Total			$312,520.00

Working note-1- Comfy Fit
	Swoop	Rufus
Contribution margin per unit (a)	5	15
Hour Required per Unit (b)	0.1	0.5
Contribution margin per Hour (a/b)	50	30
Ranking(in order of highest contribution per pound)	I	III
Maximum Unit can be Produced (d)	51260	51260
Hour Required for Maximum Unit to be produced (dXb)	5126	25630
Hour Available			7000
Hour used	5126	1874	7000
Unit can produced with available housr	51260	3748