Determining the Optimal Product Mix with One Constrained Resource Casual Essenti

ID: 2454799 • Letter: D

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 $4 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 $ 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? $

Explanation / Answer

Contribution margin per unit of Homerun = $5

Contribution margin per unit of Goalpost = $15

Machine time required

Homerun

Goalpost

Contribution margin per shirt

$15

Machine time per shirt

6 minutes

30 minutes

No. of team shirts per hour

10 (60 minutes / 6)

2 (60 minutes /30)

Contribution margin per hour

$50 ($5 * 10)

$30 ($15*2)

Maximum machine time available = 1000 hours = 60,000 minutes

Since, contribution margin for Homerun tem shirts is more, company will try to make this first.

Maximum sellable shirts for each team = 50,890

Hence, we will make 50,890 units of Homerun team first.

Unites of homerun team shirts that can be made in 60,000 units = 60,000 / 6 = 10,000

Hence optimal mix is of 10,000 homerun team shirts and zero Goalpost team shirts.

Total contribution margin earned for the optimal mix = ($5 * 10,000) + ($15 * 0) = $50,000