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 $2x^{2}+55x + 10$. the cost, in dollars, of producing the cell phones can be modeled by $2x^{2}-15x - 40$. 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 $2x^{2}+55x + 10$. the cost, in dollars, of producing the cell phones can be modeled by $2x^{2}-15x - 40$. 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

Answer:

40x - 30; $9,570

Explanation:

Step1: Find profit expression

Profit = Revenue - Cost. Revenue is $2x^{2}+55x + 10$, cost is $2x^{2}-15x - 40$. So, Profit=$ (2x^{2}+55x + 10)-(2x^{2}-15x - 40)$. [ \begin{align*} &(2x^{2}+55x + 10)-(2x^{2}-15x - 40)\ =&2x^{2}+55x + 10-2x^{2}+15x + 40\ =&(2x^{2}-2x^{2})+(55x+15x)+(10 + 40)\ =&40x-30 \end{align*} ]

Step2: Calculate profit for x = 240

Substitute $x = 240$ into the profit - expression $40x-30$. $40\times240-30=9600 - 30=9570$.