profit is the difference between revenue and cost. the revenue, in dollars, of a company that manufactures…

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

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 $P$ = Revenue $R$ - Cost $C$. Given $R = 2x^{2}+55x + 10$ and $C=2x^{2}-15x - 40$. $P=(2x^{2}+55x + 10)-(2x^{2}-15x - 40)$

Step2: Simplify the profit - expression

Expand the right - hand side: $P=2x^{2}+55x + 10 - 2x^{2}+15x + 40$. Combine like terms: $(2x^{2}-2x^{2})+(55x + 15x)+(10 + 40)=70x+50$.

Step3: Calculate profit when $x = 240$

Substitute $x = 240$ into the profit formula $P = 70x+50$. $P=70\times240+50$. First, calculate $70\times240 = 16800$. Then, $P=16800 + 50=16850$.

Answer:

$70x + 50;$16,850$