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

$5

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

`(dP)/(dx)=-4x+20`

`(dP)/(dx)=0`

`-4x+20=0`

`4x=20`

`x=5`

Again differentiate w.r.t x

`(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 .