Answer
a) Profit function $P(x) = -0.05x^3+0.8x^2+155x-500$
b) $P(15) =$\$$1836.25$
c) The profit is $\$1836.25$ when $1500$ cell phones are sold.
Work Step by Step
a) We know we can find the profit function by subtracting the cost function from the revenue function.
$P(x) = R(x) -C(x)$
$=(-1.2x^2+220x)-(0.05x^3-2x^2+65x+500)$
$=-1.2x^2+220x-0.05x^3+2x^2-65x-500$
$=-0.05x^3+0.8x^2+155x-500$
b) Given $x=15$, when substituted in profit function $P(x)$
$P(15)= -0.05(15)^3+0.8(15)^2+155(15)-500$
$=-168.75+180+2325-500$
$=$\$$1836.25$
c) When $15$ hundred cell phones are sold, the profit is $\$1836.25$
