# Math Help - Calculus Word Problem-Finding Max Profit

1. ## Calculus Word Problem-Finding Max Profit

A manufacturer of an electronic toy finds that the total daily cost c(x) of producing x toys per day is given by c(x)=500+5x+.001x^2
Each toy can be sold at a price p(in dollars) given by: p=21-.003x. If all the toys that are manufactured can be sold, find the daily level of production that will result in maximum profit.

all ive got so far is profit=21-.003x-(500+5x+.001x^2)

and for future reference how do i type my math problems on the computer and get all the signs that a regular keyboard doesn't have?

Thanks!

2. Originally Posted by Jim Marnell
A manufacturer of an electronic toy finds that the total daily cost c(x) of producing x toys per day is given by c(x)=500+5x+.001x^2
Each toy can be sold at a price p(in dollars) given by: p=21-.003x. If all the toys that are manufactured can be sold, find the daily level of production that will result in maximum profit.

all ive got so far is profit=21-.003x-(500+5x+.001x^2)

and for future reference how do i type my math problems on the computer and get all the signs that a regular keyboard doesn't have?

Thanks!
profit = revenue - cost

$P(x) = x(21 - .003x) - (500+5x+.001x^2)$

go to the Latex help forum to learn how to typeset equations/expressions

http://www.mathhelpforum.com/math-help/latex-help/

3. Do i have to anything else with this problem or is $p(x)=x(21-.003x)-(500+5x+.oo1x^2$ the answer?

Thanks!

4. Originally Posted by Jim Marnell
Do i have to anything else with this problem or is $p(x)=x(21-.003x)-(500+5x+.oo1x^2$ the answer?

Thanks!
... find the daily level of production that will result in maximum profit.
... don't you have to find the value of x that will maximize the profit?

5. yea, I'm just confused on what that means. Do i take the derivative of that function?

6. Originally Posted by Jim Marnell
yea, I'm just confused on what that means. Do i take the derivative of that function?
that would be the correct first step in finding a maximum.

7. I'm still having problems with this if anyone can help, it would be greatly appreciated! Heres what i have so far:
Profit= $x(21-.003x)-(500+5x+.001x^2$
Profit= $x(-479-5.003x-.001x^2$--Not sure if this was added up correctly
Profit= $-479x-5.003x^2-.001x^3$
$Profit'=-479-10.006x-.003x^2$

I dont know if i'm even doing this right
Thanks for any help!

8. $P(x) = x(21 - .003x) - (500+5x+.001x^2)$

$P(x) = 21x - .003x^2 - 500 - 5x - .001x^2$

combine like terms ...

$P(x) = -.004x^2 + 16x - 500$

$P'(x) = -.008x + 16$

set $P'(x) = 0$

$x = 2000$

9. ahh i see what i was doing wrong, i was applying that x and distributing it 2 both parts of the function. I appreciate the help!