Williams Gear makes and sells three types of computer laptop sleeves: leather, fabric, and plastic. Management is trying to determine the most profitable mix. Sales prices, demand, and use of manufacturing inputs follow:

Leather Fabric Plastic

Sales price $ $160$ $ $70$ $ $40$

Maximum quarterly demand $($sleeves$)2,50012,50020,000$

Input requirements per unit

Direct material quantity per sleeve $($ounces$)16610$

Direct material price per ounce of material $ $4\mathrm{.}25$ $ $6\mathrm{.}00$ $ $2\mathrm{.}20$

Direct labor quantity per sleeve $($hours$)0\mathrm{.}90\mathrm{.}40\mathrm{.}3$

Direct labor price per hour $ $35$ $ $35$ $ $35$

Other Costs

Variable costs

Factory overhead $ $5$ per direct labor$-$hour

Marketing $ $6\%$ of sales price

Quarterly fixed costs

Manufacturing $ $70,000$

Marketing $ $15,000$

Administration $ $60,000$

Williams has two production limits: $(1)$ the demand for the individual sleeves $($see maximum quarterly demand$)$ and $(2)10,000$ direct labor$-$hours per quarter caused by the physical layout of the production area.

Required:

a$-1.$ Assuming the company can satisfy the annual demand, calculate the contribution margin for each type of sleeve using the table below.

a$-2.$ How much operating profit could Williams earn if it were able to satisfy the annual demand?

b$-1.$ Compute the contribution margin for each sleeve per the constrained resource, direct labor.

b$-2.$ Which of the three product lines makes the most profitable use of the constrained resource, direct labor?

c$.$ Given the information so far, what product mix do you recommend?

d$-1.$ Calculate the contribution margin for each type of sleeve using the product mix recommended in requirement c$.$

d$-2.$ How much operating profit should your recommended product mix generate?

e$.$ Suppose that the company could expand its labor capacity by leasing a new stitching machine that will free up $2,160$ direct labor hours per quarter. What is the maximum quarterly lease payment that Williams Gear would be willing to pay?

f$.$ Suppose the company selling the stitching machine is not quite sure without further analysis how many direct labor hours the new machine would free up$.$ Regardless of the number of new hours, what is the maximum quarterly lease payment Williams Gear would be willing to pay?