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 30 minutes of machine time.

Assume that a maximum of 47,860 units of each sweatshirt 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 sweatshirt?

2. What is the optimal mix of sweatshirt?

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

Explanation / Answer

1 Contribution Margin Swoop Rufus Contribution margin per unit 5 15 Time Required Per Unit 6 Min 30 Min In Hours .10 Hour .50 Hour Contribution Per Hour 50 30 I Ii Contribution Margin Swoop 50 Rufus 150 Optimal Mix Total Available Hours = 1000*7 7000 Hours Swoop Rufus Units 47860 4428 Hours 4786 2214 Contribution 4786*50 239300 2214*30 66420 Total Contribution Margin 305720

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