Using the bottleneck method, what is the profit if the company manufactures the optimal product mix $($consider variable costs only$-$overhead is not included in this profit calculation$)?$

A$)$ $$8,490$

B$)$ $$9,654$

C$)$ $$7,952$

D$)$ $$8,607$

E$)$ $$11,249$

F$)$ $$6,782$

G$)$ $$6\mathrm{.}045$

Planning

A company makes four products that have the following characteristics: Product A sells for $$45$ but needs $$12$ of materials and $$11$ of labor to produce; Product B sells for $$80$ but needs $$25$ of materials and $$15$ of labor to produce; Product $C$ sells for $$75$ but needs $$30$ of materials and $$15$ of labor to produce; Product D sells for $$120$ but needs $$75$ of materials and $$10$ of labor to produce. The processing requirements for each product on each of the four machines are shown in the table.

$\backslash$table$[[,$Processing Time $($min$/$unit$)],[$Work Center,A$,$B$,$C$,$D$],[$W$,12,2,3,12],[x,9,7,4,8],[Y,4,3,12,9],[Z,7,10,5,10]]$

Work centers W$,$ X$,$ Y$,$ and Z are available for $40$ hours per week and have no setup time when switching between products. Market demand for each product is $80$ units per week. In the questions that follow, the traditional method refers to maximizing the contribution margin per unit for each product, and the bottleneck method refers to maximizing the contribution margin per minute at the bottleneck for each product.