Question

A small company shows the profits from their business with the function ​P(x)0.01x^2+60x-​500, where x is the number of units they sell and P is the profit in dollars.
a. How many units are sold by the company to earn the maximum​ profit?
b. Between which numbers of units sold does the company show a​ profit?

Answer 1

Answer:

A, 3,000 B 8,5992

Step-by-step explanation:

:)

Answer 2

Answer:

Step-by-step explanation:

$a)\ \frac{dP}{dx}=0.02x+60=0,\ \frac{d^2P}{d^2x}=0.02\\ \\ \text{Since acceleration is always positive there is no maximum profit point, profit will always be increasing as more units are sold.}\\ \\ 0.01x^2+60x-500>0\\ \\ x>8.3\\ \\ \text{So the company will start to profit when it sells its 9th unit. I suspect by the questions asked that maybe the profit function provided may be a typo. It seems weird to ask for a maximum profit when there is no such thing for the equation given.}$