Question

Determining the Optimal Product Mix with One Constrained Resource

Casual Essentials, Inc. manufactures two types of team shirts, the Homerun and the Goalpost, with unit contribution margins of $6 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 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 team shirts?

Contribution Margin

Homerun ____ units  ?

Goalpost ____ units ?

2. What is the optimal mix of team shirts?

Optimal Mix

Homerun ___ units ?

Goalpost ___ units ?

3. What is the total contribution margin earned for the optimal mix?

Answer 1

1)
	Contribution Margin
Homerun     = Contribution margin x Units per hour     = $ 6 x ( 60 min / 6 min )     = $ 6 x 10	$ 60
Goalpost     = Contribution margin x Units per hour     = $ 15 x ( 60 min / 30 min )     = $ 15 x 2	$ 30
2)
Total machine hours       = 7 machines x 1,000 Hours	7,000 hours
	Optimal mix
Homerun          = 7,000 hours x ( 60 min / 6 )	70,000 Units
Goalpost	0 Units
3)
Total Contribution margin        =   Total Units x Contribution margin        = 70,000 units x $ 6	$ 420,000

answered by: anonymous