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Math Help - Calculus Word Problem-Finding Max Profit

  1. #1
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    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!
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  2. #2
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    Quote Originally Posted by Jim Marnell View Post
    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/
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    Do i have to anything else with this problem or is p(x)=x(21-.003x)-(500+5x+.oo1x^2 the answer?

    Thanks!
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  4. #4
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    Quote Originally Posted by Jim Marnell View Post
    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?
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    yea, I'm just confused on what that means. Do i take the derivative of that function?
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  6. #6
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    Quote Originally Posted by Jim Marnell View Post
    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.
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  7. #7
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    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!
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  8. #8
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    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
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  9. #9
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    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!
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