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 50,890 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?
2. What is the optimal mix of team shirts?
3. What is the total contribution margin earned for the optimal mix?

1. What is the contribution margin per hour of machine time for each type of team shirts?

Homerun = $ 50

Goalpost =  $30

2. What is the optimal mix of team shirts?

Homerun =  50,890

Goalpost  = 3,822

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

Total contribution margin earned for the optimal mix = $311,780

Explanation:

1. Contribution margin per hour of machine time for each type of team shirts

Homerun

Contribution margin per hour of machine = $5 / (6/60)

                                                                     =  $ 50

Goalpost

Contribution margin per hour of machine = $15 / (30/60)

                                                                     =  $30

2. Optimal mix of team shirts

Determine if machine time is a limiting factor

Demanded Hours

Homerun 0.1 × 50,890  = 5,089

Goalpost 0.5 × 50,890  = 25445

Total Hours Demanded = 30,534

Available Hours

Available hours =1,000 hour × 7 machines

                          =7,000 hours

Demanded Hours > Available hours

Therefore  machine time is a limiting factor

Determine Mix

Rank the T-Shirts based on contribution margin per hour of machine time

Position 1. Homerun = 5,089

Position 2. Goalpost  = 1,911 (takes the remaining hours)

Number of T-Shirts (mix)

Homerun = 5,089 / 0.1 =  50,890

Goalpost  = 1,911 / 0.5 =  3,822

3. The total contribution margin earned for the optimal mix

Homerun =  50,890 × $5 =254,450

Goalpost  =  3,822 × $15 = 57,330

Total                                 = 311,780

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