Alpena Corporation manufactures smartphone and tablet cases. The following is the cost of each unit.

Materials $ $7\mathrm{.}40$

Labor $3\mathrm{.}00$

Variable overhead $1\mathrm{.}00$

Fixed overhead $($$$1,740,000$ per year; $150,000$ units per year$)11\mathrm{.}60$

Total $ $23\mathrm{.}00$

Decatur Devices has approached Alpena with an offer to buy $3,000$ cases at a price of $$17\mathrm{.}90$ each for its new specialty tablet designed for health care workers. The regular price of an Alpena case is $$27\mathrm{.}00.$ Alpena has the total capacity to produce $180,000$ units without increasing its fixed overhead. Decatur Devices requires that each case use its branding, which requires a more expensive embossing step. This will result in an additional $$2\mathrm{.}90$ per case labor cost. The material cost of of the Decatur case will be the same as for the current models. The Decatur order will also require a one$-$time rental of embossing equipment for $$6,336.$

Required:

a$.$ Prepare a schedule to show the impact of filling the Decatur Devices order on Alpena$$s profits for the year.

b$.$ Would you recommend that Alpena accept the order?

c$.$ Considering only profit, determine the minimum quantity of cases in the special order that would make it profitable, assuming capacity is available.