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 $51,720$ 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?

Contribution Margin

Swoop $fill in the blank $1$

$50$

Rufus $fill in the blank $2$

$45$

$2.$ What is the optimal mix of sweatshirt?

Optimal Mix

Swoop fill in the blank $3$

$70,000$

units

Rufus fill in the blank $4$

$70,000$

units

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