Determining the Optimal Product Mix with One Constrained Resource and a Sales Co

Question

Determining the Optimal Product Mix with One Constrained Resource and a Sales Constraint

Comfy Fit Company manufactures two types of university sweatshirts, the Swoop and the Rufus, with unit contribution margins of $5 and $15, respectively. Regardless of type, each sweatshirt must be fed through a stitching machine to affix the appropriate university logo. The firm leases seven machines that each provides 1,000 hours of machine time per year. Each Swoop sweatshirt requires 6 minutes of machine time, and each Rufus sweatshirt requires 20 minutes of machine time.

Assume that a maximum of 40,000 units of each sweatshirt can be sold.

Required:

1. What is the contribution margin per hour of machine time for each type of sweatshirt? When computing your answers, round machine time per unit to two decimal places. Round your final answers to the nearest dollar.

2. What is the optimal mix of sweatshirts? When computing your answers, round machine time per unit to two decimal places. Round your final answers to the nearest whole unit.

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

Explanation / Answer

1 Swoop Rufus Unit Contribution Margin 5 15 Machine hours rquired per unit 0.1 0.3333 Contribution margin per hour 50 45 2 Optimal Mix Swoop 40000 Rufus 9000 =(7000-40000*0.1)/0.3333 3 Total contribution margin earned for the optimal mix=(40000*5)+(9000*15)= $335000

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