Question

A company has determined that when x items are sold daily, the profit P is given by

P(x)=-0.002x^2+4.3x-120

What is the profit if 700 items are made?
How many items should be made daily in order to maximize the companys profit?

I know the first one is 1,910, but how do I maximize the company's profit?

Answer 1

This basically asks you to find the vertex of the equation

Answer 2

find the derivative and set it to zero

Answer 3

solve for x then

Answer 4

What formula would I use?

Answer 5

I don't know any formulas but I do know how to find it using a derivative

Answer 6

Ok, any advice on how I should proceed?

Answer 7

Find the derivative

Answer 8

So if I get a derivative of 4.3-0.004x, what should I do then?

Answer 9

set it to zero and solve for x

Answer 10

4.3-0.004x=0

Answer 11

4.3-0.004x=0
-0.004x=-4.3
x=-4.3/-0.004
x=1075

Answer 12

1075 items

Answer 13

i see, so the derivative is the key, awesome, thanks!

Answer 14

http://www.wolframalpha.com/input/?i=-0.002x%5E2%2B4.3x-120

if you graph it you can see the highest point right?

That point is called the vertex and you can find it using the derivative

Answer 15

Ah, ok I got you.