Question

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. Contribution Margin Swoop $ 50 A Rufus A 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. Optimal Mix Swoop X units Rufus X units 3. What is the total contribution margin earned for the optimal mix?

Answer 1

Requirement a: Calculate contribution margin per hour as follows: Rufus 20 AB Swoop Time required by 1 unit 2 (in minutes) Number of units can produce in 3 1 hour (i.e., 60 minutes) 4 Contribution margins per units 5 Contribution margin per hour $15 $45 Calculations are as shown below: в с Swoop Rufus Time required by 1 unit 2 (in minutes) 20 Number of units can produce in 3 1 hour (i.e., 60 minutes) =60/B2 =60/C2 4 Contribution margins per units 5 5 Contribution margin per hour =B4*B3 =C4*C3 13

Requirement b: Step 1: Calculate total time available as follows: Total time available = 7 machine x 1,000 hours per machine = 7,000 hours Step 2: Calculate Maximum units that can be produced for Swoop as follows: Total time available for Swoop Maximum units of Swoop= Machine time per Swoop's unit 7,000 hours 6 minutes per Swoop 60 minutes 7,000 hours 0.10 = 70.000 units Maximum units that can be produced for Swoop is 70.000. However, maximum units that can be sold limits to 40,000 units. Thus, an optimal mix will not contain any unit more than the number of units that can be sold. Therefore, optimal mix will consist of 40,000 units of Swoop.

Step 3: Calculate balance time left for producing Rufus as follows: Balance time left | = Total time available - Time consumed by Swoop of machine (40,000 < 6 minutes) =(1,000 hours x 7) - 60 minutes = 3.000 hours Step 4: Calculate Maximum units that can be produced for Rufus as follows: Total time available for Rufus Maximum units of Rufus = Machine time per Rufus' unit 3.000 hours ( 20 minutes per Rufus 60 minutes 3,000 hours 0.33 = 9,091 units Therefore, optimal mix will consist of 9,091 units of Rufus. Requirement c: Calculate total contribution margin earned at optimal mix as follows:

Calculate total contribution margin earned at optimal mix as follows: Swoop $5 Contribution margins per units (1) Optimal mix units (2) Total contribution margin (1 x 2) Rufus $15 9091 $136,365 $336,365 40000 $200,000