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.

1. What is the contribution margin per hour of machine time for the Swoop sweatshirts? Round intermediate calculations to 4 decimal places and round your final answer to the nearest dollar, if rounding is required. $

   What is the contribution margin per hour of machine time for the Rufus sweatshirts? Round intermediate calculations to 4 decimal places and round your final answer to the nearest dollar, if rounding is required. $

2. What is the optimal mix of sweatshirts? Round intermediate calculations to 2 decimal places. Round your final answer to the nearest whole unit, if rounding is required

   Now the optimal mix is units of Swoop sweatshirts and units of Rufus sweatshirts.

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