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 there are no other constraints.
Required:
a. 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.
b. 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.
c. What is the total contribution margin earned for the optimal mix?

Answer 1

Answer:

1. Swoop = $50

Rufus = $45

2. Optima mix = 40, 000 units of Swoop and 9, 091 units of Rufus

3. $336, 365

Explanation:

We will assume that a maximum of 40, 000 units of each sweat shirts can be sold.

1. Contribution margin is the selling price minus all the variable costs associated with the product. The total contribution margin represents the amount of earnings that are available to pay for fixed costs after paying for variable costs.

                                                                   Swoop    Rufus

Contribution per margin            $ 5    $ 15

Required machine time per unit^      0.10           0.33

Contribution margin per machine time $50    $45

^ 0.10 = 6 minutes per Swoop units / 60 minutes

0.33 = 20 minutes per Rufus unit / 60 minutes

2. Optimal product mix refers to the variety of products that a business offers to its customers. Companies determine their optimal mix for their business as this optimizes the potential unit sales while maintaining or improving the company’s profitability.

Since Swoop yields the highest contribution margin per hour of machine time [$50], we will prioritize producing all pf the Swoop T-shirts that the market can take, i.e. to meet the demand.  

Machine time required for the maximum amount of Swoop = 40, 000 x 0.1 hours = 4, 000 hours needed to manufacture the Swoop t-shirts.  

The remaining machine hours will manufacture the Rufus T-shirts.

7, 000 – 4, 000 = 3, 000 hours.

3, 000 / 0.33 = 9, 091 units.

Therefore, the optimal mix is 40, 000 units of Swoop sweat shirts and 9, 091 units of Rufus sweat shirts. This will take up all the machine hours available.

3. Total contribution margin for the optima mix = (40, 000 x $5) + (9, 091 x $15) = $336, 365