Question

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

Explanation:

Step1: Encontrar la expresión del profit

El profit es la diferencia entre el ingreso (revenue) y el costo (cost). El ingreso está dado por $2x^{2}+55x + 10$ y el costo por $2x^{2}-15x - 40$.
$(2x^{2}+55x + 10)-(2x^{2}-15x - 40)=2x^{2}+55x + 10 - 2x^{2}+15x + 40$.
Combinando términos semejantes: $(2x^{2}-2x^{2})+(55x + 15x)+(10 + 40)=70x+50$.

Step2: Calcular el profit para $x = 240$

Sustituir $x = 240$ en la expresión del profit $70x+50$.
$70\times240+50=16800 + 50=\$16,850$.

Answer:

C. $70x + 50$, $\$16,850$