Determining the Optimal Product Mix with One Constrained Resource and a Sales Constraint

Casual Essentials, Inc. manufactures two types of team shirts, the Homerun and the Goalpost, with unit contribution margins of $$5$ and $$15,$ respectively. Regardless of type, each team shirts must be fed through a stitching machine to affix the appropriate team logo$.$ The firm leases seven machines that each provides $1,000$ hours of machine time per year. Each Homerun shirt requires $6$ minutes of machine time, and each Goalpost shirt requires $30$ minutes of machine time.

Assume that a maximum of $48,630$ units of each team shirts 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 team shirts?

Contribution Margin

Homerun $fill in the blank $1$

Goalpost $fill in the blank $2$

$2.$ What is the optimal mix of team shirts?

Optimal Mix

Homerun fill in the blank $3$

units

Goalpost fill in the blank $4$

units

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

$fill in the blank $5$