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 $68,000$ $ $31\mathrm{.}00$ $ $4\mathrm{.}50$ $ $4\mathrm{.}20$

Trish $60,000$ $ $5\mathrm{.}00$ $ $1\mathrm{.}40$ $ $0\mathrm{.}77$

Sarah $53,000$ $ $44\mathrm{.}50$ $ $9\mathrm{.}14$ $ $6\mathrm{.}30$

Mike $34,000$ $ $17\mathrm{.}00$ $ $3\mathrm{.}80$ $ $4\mathrm{.}90$

Sewing kit $343,000$ $ $9\mathrm{.}80$ $ $5\mathrm{.}00$ $ $0\mathrm{.}42$

The following additional information is available:

The company$$s plant has a capacity of $127,580$ direct labor$-$hours per year on a single$-$shift basis. The company$$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 $$565,000$ per year. Variable overhead costs are $$5$ 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:

$4.$ 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 $127,580$ 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$)?$