Sigma Company produces three versions of a brass desk lamp: basic, custom, and deluxe. The planned production information for the upcoming month follows:

Resources $-$Cost per Month$-$ Fringe Benefits$-$ Total $-$Hours per Month

Direct labor: $$4,270-$$$1000-$ $$5,270-150$

Indirect labor cost : $$4,210-$$$800-$$$5,010-150$

Machinery: $$70,000--$$$70,000-250$

Basic$-$Custom$-$Deluxe

Selling price per unit: $$200-$$$220-$$$530$

Direct materials cost per unit: $$60-$$$70-$$$85$

Production Information: Basic$-$Custom$-$Deluxe

Production and sales volume $($units$)$: $4,500-3,200-1,200$

Direct labor hours per unit: $2\mathrm{.}00-2\mathrm{.}50-3\mathrm{.}00$

Total direct labor hours: $9,000-8,000-3,600$

Machine hours per unit: $0\mathrm{.}05-0\mathrm{.}08-0\mathrm{.}09$

Total machine run time $($hours$)$: $225-256-108$

Number of production runs: $12\mathrm{.}00-10\mathrm{.}00-8\mathrm{.}00$

Setup time per production run $($machine hours$)$: $2\mathrm{.}00-1\mathrm{.}00-2\mathrm{.}50$

Total setup time $($machine hours$)$: $24\mathrm{.}00-10\mathrm{.}00-20\mathrm{.}00$

Total machine hours: $249-266-128$

Indirect labor data Basic$-$Custom$-$Delux

Setup time per run $($hours$)$: $3\mathrm{.}00-4\mathrm{.}00-6\mathrm{.}00$

Number of employees per setup: $4-4-4$

Indirect labor hours per setup: $12\mathrm{.}00-16\mathrm{.}00-24\mathrm{.}00$

In order to meet anticipated demand for the upcoming month, Sigma Company plans to rent three machines, each costing $$70,000$ per month, and hire four indirect workers, each costing $$5,010$ per month. The total cost of the three machines and four indirect workers comprises the total overhead cost at Sigma Company.

Required

a$)$ Given the production plan, what is the deluxe product$$s planned total contribution margin?

b$)$ If Sigma Company computes a plantwide rate to allocate total overhead cost to the three products by dividing the sum of indirect labor cost and machine cost by planned total direct labor hours, what is the total overhead cost that will be allocated to the deluxe product, and what will be its resulting gross margin?

c$)$ If Sigma Company uses TDABC to allocate the indirect labor cost and the machine cost to the three products, what will be the total overhead cost allocated to the deluxe product, and what will be its resulting gross margin?