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 48,900 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	$
Goalpost	$

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 per hour from Homerun = No. of units per hour x contribution margin per unit

= 10 x $5 = $50

Contribution margin per hour from Goalpost = No. of units per hour x contribution margin per unit

= 2 x $15 = $30

2. Total number of hours available during a year = 7 x 1,000 hours = 7,000 hours

Maximum number of units of each type to be sold = 48900

Hours utilized in producing 48900 units of Homerun = (48900*6 minutes) / 60 minutes = 4890

Out of 7,000 available hours, 4890 hours must be used to produce Homerun.

Number of units of Goalpost to be produced = Available hours x unit per hour = 2110*2 = 4220

Thus, the optimal mix of shirts is as follows:

Homerun = 48900 units

Goalpost = 4220 units

3. Total contribution margin earned for the optimal mix = (No. of units of Homerun x Contribution margin) + (No. of units of Goalpost x Contribution margin)

= (48900*5)+(4220*15)

= $307800