Problem $11-25($Algo$)$ Volume Trade$-$Off Decisions $[$LO$11-5,$ LO$11-6]$

The Walton Toy Company manufactures a line of dolls and a sewing kit. Demand for the company$$s products is increasing, and management requests assistance from you in determining an economical sales and production mix for the coming year. The company has provided the following data:

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

Debbie $52,000$ $ $17\mathrm{.}00$ $ $4\mathrm{.}50$ $ $2\mathrm{.}80$

Trish $44,000$ $ $6\mathrm{.}50$ $ $1\mathrm{.}30$ $ $1\mathrm{.}40$

Sarah $37,000$ $ $26\mathrm{.}00$ $ $6\mathrm{.}74$ $ $4\mathrm{.}90$

Mike $40,800$ $ $12\mathrm{.}00$ $ $2\mathrm{.}20$ $ $3\mathrm{.}50$

Sewing kit $327,000$ $ $8\mathrm{.}20$ $ $3\mathrm{.}40$ $ $1\mathrm{.}05$

The following additional information is available:

The company$$s plant has a capacity of $114,750$ direct labor$-$hours per year on a single$-$shift basis. The company$$s present employees and equipment can produce all five products.

The direct labor rate of $$7$ per hour is expected to remain unchanged during the coming year.

Fixed manufacturing costs total $$540,000$ per year. Variable overhead costs are $$4$ 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:

$1.$ How many direct labor hours are used to manufacture one unit of each of the company$$s five products?

$2.$ How much variable overhead cost is incurred to manufacture one unit of each of the company$$s five products?

$3.$ What is the contribution margin per direct labor$-$hour for each of the company$$s five products?

$4.$ Assuming that direct labor$-$hours is the company$$s constraining resource, what is the highest total contribution margin that the company can earn if it makes optimal use of its constrained resource?

$5.$ Assuming that the company has made optimal use of its $114,750$ direct labor$-$hours, what is the highest direct labor rate per hour that Walton Toy Company would be willing to pay for additional capacity $($that is$,$ for added direct labor time$)?$