Thread: 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!

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



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

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

Do i have to anything else with this problem or is the answer?

Thanks!

Originally Posted by Jim Marnell

Do i have to anything else with this problem or is 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?

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

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.

I'm still having problems with this if anyone can help, it would be greatly appreciated! Heres what i have so far:
Profit=
Profit= --Not sure if this was added up correctly
Profit=


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

combine like terms ...





set

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!