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? o 40x - 30; $2,400 o 40x - 30; $9,570 o 70x + 50; $16,850 o 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? o 40x - 30; $2,400 o 40x - 30; $9,570 o 70x + 50; $16,850 o 70x + 50; $28,800

Answer

Explanation:

Step1: Find profit formula

Profit $P$ = Revenue $R$ - Cost $C$. Given $R = 2x^{2}+55x + 10$ and $C=2x^{2}-15x - 40$. Then $P=(2x^{2}+55x + 10)-(2x^{2}-15x - 40)$. [ \begin{align*} P&=2x^{2}+55x + 10-2x^{2}+15x + 40\ &=(2x^{2}-2x^{2})+(55x+15x)+(10 + 40)\ &=70x+50 \end{align*} ]

Step2: Calculate profit for $x = 240$

Substitute $x = 240$ into the profit formula $P = 70x+50$. So $P=70\times240+50$. $P = 16800+50=16850$.

Answer:

$70x + 50;$16,850$