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 50,950 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

Q. 1	Contriubtion margin per hour of maching time
contriubtion margin per hour	Contribution margin per pc X total pcs fed through maching
swoop	6 mts of machine time per pc
	in 1 hour	60 mts / 6 mts per pc.	10 pcs in 1 hour
contriubtion margin per hour	10 Pcs of Swoop X 5$	50 USD per hour contribution margin
Rufus	30 mts of machine time per pc
	in 1 hour	60 mts / 30 mts per pc.	2 pcs in 1 hour
contriubtion margin per hour	2 Pcs of Swoop X 15$	30 USD per hour contribution margin

it is more profitable to stitch swoop since contribution margin is 50 USD per hour.

2. What is the optimal mix of sweatshirt?

	Optimal Mix
Swoop	Units first priority will be given to full capacity upto 50,950 units, since contribution margin is high per hour here.
For balance hour Rufus	Units will be produced.

Q. 2	Optimal mix
Total available hours	7 machines	X 1000 per machine hrs.	7,000 hours
Hours USED For Swoop	=50950 X 6 /60	5095	Hours used
Balance hours for Rufus	7000 - 5095	1905
Rufus can be produced	balance hours / 30 minutes
	=1905hours / 30 minutes for per pc	3810
Optimal MIX
Swoop	50950 Pcs
Rufus	3810 Pcs
Q. 2	Optimal mix Contriubtion Margin
Swoop	50950 Pcs	X 5 =	2,54,750
Rufus	3810 Pcs	X 15 =	57,150
Total Contribution margin for optimal mix		3,11,900