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 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

Explanation:

Step1: Encontrar la expresión del profit

El profit $P$ es la diferencia entre el ingreso $R$ y el costo $C$. Dado que $R = 2x^{2}+55x + 10$ y $C=2x^{2}-15x - 40$, entonces $P=R - C=(2x^{2}+55x + 10)-(2x^{2}-15x - 40)$.
Eliminando los paréntesis: $P=2x^{2}+55x + 10 - 2x^{2}+15x + 40$.
Combinando términos semejantes: $P=(2x^{2}-2x^{2})+(55x + 15x)+(10 + 40)=70x + 50$.

Step2: Calcular el profit para $x = 240$

Sustituir $x = 240$ en la expresión del profit $P = 70x+50$.
$P=70\times240 + 50$.
$70\times240=16800$, entonces $P=16800 + 50=16850$.

Answer:

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