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

Answer

Explanation:

Step1: Define profit formula

Profit = Revenue - Cost

Step2: Substitute given polynomials

Profit = $(2x^2 + 55x + 10) - (2x^2 - 15x - 40)$

Step3: Simplify the expression

$2x^2 + 55x + 10 - 2x^2 + 15x + 40 = 40x + 50$ Wait, correction: $10 + 40 = 50$, $55x +15x=70x$, $2x^2-2x^2=0$. So Profit = $70x + 50$

Step4: Calculate profit at x=240

Profit = $70(240) + 50 = 16800 + 50 = 16850$

Answer:

70x + 50; $16,850