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 50,280 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	$50
Goalpost	$30

2. What is the optimal mix of team shirts?

	Optimal Mix
Homerun	50890??? units
Goalpost	3822??? units

3. What is the total contribution margin earned for the optimal mix?
$311,780???

Answer 1

• Requirement 1 is CORRECT
• Requirement 2
  >Total Hours available = 1000 hours per machine x 7 machines = 7000 hours

>Working

--Homerun has MORE contribution margin ($50) per hour than Goalpost ($30) per hour and hence HOMERUN should be given first preference to produce.

A	Total hours available	7000
B	Maximum units for Homerun	50280
C	Hours per unit required for Homerun	0.1
D = B x C	Total Hours required	5028
E = A- D	Remaining hours	1972
F	Hours per unit required for Goalpost	0.5
G = E/F	Total units for Goalpost	3944

>Requirement: Optimal Mix
Homerun = 50280 units
Goalpost = 3944 units

• Requirement 3

Total Contribution margin = (50280 units x 0.1 hr x $ 50 per hour) + (3944 units x 0.5 hours x $ 30 per hour)
= 251400 + 59160
= $ 310,560 Answer