profit is the difference between revenue and ...
profit is the difference between revenue and cost. the revenue, in dollars, of a company that manufactures cell - phones can be modeled by the polynomial 2x² + 55x + 10. the cost, in dollars, of producing the cell phones can be modeled by 2x² - 15x - 40. the variable x represents the number of cell phones sold. what expression represents the profit, and what is the profit if 240 cell phones are sold? 40x - 30; $2,400 40x - 30; $9,570 70x + 50; $16,850 70x + 50; $28,800
Answer
# Explanation:
## Step1: Find profit - expression formula
Profit $P(x)=R(x)-C(x)$, where $R(x)$ is revenue and $C(x)$ is cost. Given $R(x)=2x^{2}+55x + 10$ and $C(x)=2x^{2}-15x - 40$.
## Step2: Calculate the profit - expression
$P(x)=(2x^{2}+55x + 10)-(2x^{2}-15x - 40)=2x^{2}+55x + 10 - 2x^{2}+15x + 40=(2x^{2}-2x^{2})+(55x + 15x)+(10 + 40)=70x+50$.
## Step3: Calculate the profit when $x = 240$
Substitute $x = 240$ into $P(x)=70x + 50$. Then $P(240)=70\times240+50=16800 + 50=16850$.
# Answer:
$70x + 50; \$16,850$