A toilet manufacturer has decided to come out with a new and improved toilet. The fixed cost for the production of this new toilet line is $16,600 and the variable costs are $69 per toilet. The Company expects to sell the toilets for $157. Formulate a function P(x)for the total profit from the Production and sale of x toilets.
A) $ P(x)=88 x+16600 $
B) $ P(x)=88 x $
C) $ P(x)=88 x-16600 $
D) $ P(x)=157 x-16600 $

Question

A toilet manufacturer has decided to come out with a new and improved toilet. The fixed cost for the production of this new toilet line is $16,600 and the variable costs are $69 per toilet. The Company expects to sell the toilets for $157. Formulate a function P(x)for the total profit from the Production and sale of x toilets. 
A) $ P(x)=88 x+16600 $
B) $ P(x)=88 x $
C) $ P(x)=88 x-16600 $
D) $ P(x)=157 x-16600 $

Quizplus · Accepted Answer

The total profit function, $P(x)$, is calculated by subtracting the total costs from the total revenue. The total revenue from selling $x$ toilets is $157x$ (selling price times quantity), and the total cost is the sum of fixed costs ($16,600) and variable costs ($69 per toilet times quantity $x$), which is $16600 + 69x$. Therefore, $P(x) = 157x - (16600 + 69x) = 88x - 16600$.

A Toilet Manufacturer Has Decided to Come Out with a New