Determining the Optimal Product Mix with One Constrained Resource

Comfy Fit Company manufactures two types of university sweatshirts, the Swoop and the Rufus, with unit contribution margins of $$10$ and $$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 there are no other constraints.

Required:

If required, round your answers to the nearest whole number. If an amount is zero, enter $"0".$

$1.$ What is the contribution margin per hour of machine time for each type of sweatshirt?

Contribution Margin

Swoop $

Rufus $

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

Optimal Mix

Swoop fill in the blank $3$

units

rufus fill in the blank $4$

units

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