Question

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

Casual Essentials, Inc. manufactures two types of team shirts, the Homerun and the Goalpost, with unit contribution margins of $5 and $15, respectively. Regardless of type, each team shirts must be fed through a stitching machine to affix the appropriate team logo. The firm leases seven machines that each provides 1,000 hours of machine time per year. Each Homerun shirt requires 6 minutes of machine time, and each Goalpost shirt requires 30 minutes of machine time.

Assume that a maximum of 49,830 units of each team shirts 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 team shirts?

	Contribution Margin
Homerun	$fill in the blank 1
Goalpost	$fill in the blank 2

2. What is the optimal mix of team shirts?

	Optimal Mix
Homerun	fill in the blank 3 units
Goalpost	fill in the blank 4 units

3. What is the total contribution margin earned for the optimal mix?
$fill in the blank 5

Answer 1

1
	Homerun	Goalpost
Unit contribution margin	5	15
Divide by Machine hours	0.1	0.5
Contribution margin per hour	50	30
2
Total machine hours	7000	=7*1000
Homerun should be produced first
Hours required for Homerun	4983	=49830*0.1
Remaining hours	2017	=7000-4983
Units of Goalpost	4034	=2017/0.5
Optimal Mix
Homerun	49830	units
Goalpost	4034	units
3
Total Contribution margin	309660	=(49830*5)+(4034*15)