Problem $13-27($Algo$)$ Volume Trade$-$Off Decisions $[$LO$13-5,$ LO$13-6]$

The Walton Toy Company manufactures four dolls and a sewing kit. It provided the following data for next year:

Product Demand Next year $($units$)$ Selling Price per Unit Direct Materials Direct Labor

Debbie $61,000$ $ $20\mathrm{.}00$ $ $5\mathrm{.}40$ $ $3\mathrm{.}60$

Trish $53,000$ $ $6\mathrm{.}50$ $ $2\mathrm{.}20$ $ $1\mathrm{.}44$

Sarah $46,000$ $ $33\mathrm{.}50$ $ $8\mathrm{.}09$ $ $6\mathrm{.}30$

Mike $44,400$ $ $14\mathrm{.}00$ $ $3\mathrm{.}10$ $ $4\mathrm{.}50$

Sewing kit $336,000$ $ $9\mathrm{.}10$ $ $4\mathrm{.}30$ $ $0\mathrm{.}99$

The following additional information is available:

The company$$s plant has a capacity of $113,140$ direct labor$-$hours per year on a single$-$shift basis. Each employee and piece of equipment are capable of making all five products.

Next year$$s direct labor pay rate will be $$9$ per hour.

Fixed manufacturing costs total $$630,000$ per year. Variable overhead costs are $$2$ per direct labor$-$hour.

All of the company$$s nonmanufacturing costs are fixed.

The company$$s finished goods inventory is negligible and can be ignored.

Required:

How many direct labor$-$hours are used to manufacture one unit of each of the company$$s five products?

How much variable overhead cost is incurred to manufacture one unit of each of the company$$s five products?

What is the contribution margin per direct labor$-$hour for each of the company$$s five products?

Assuming direct labor$-$hours is the company$$s constraining resource, what is the highest total contribution margin the company can earn next year if it makes optimal use of its constrained resource?

Assuming next year the company makes optimal use of its $113,140$ direct labor$-$hours, what is the highest direct labor rate per hour Walton Toy Company should be willing to pay for additional capacity $($that is$,$ for added direct labor time$)?$