Question

Lily is making mittens for her friends. Her profit equation is P=-2x squared+20x+0, where P is her profit for the day, and x is how much she charges per pair of mittens. How much should Lilly charge per pair of mittens to make her max profit?

Answer 1

Answer:

$5

Step-by-step explanation:

We are given that  profit equation

$P(x)=-2x^2+20x+0$

Where x=Charges per pair of mittens

We have to find the charge per pair of mittens to make her max profit.

Differentiate equation w.r.t x

$\frac{dP}{dx}=-4x+20$

$\frac{dP}{dx}=0$

$-4x+20=0$

$4x=20$

$x=5$

Again differentiate w.r.t x

$\frac{d^2P}{dx^2}=-4<0$

Hence, the profit is maximum at x=5

Lily should charge $5 per pair of mittens to make her max profit .