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Math Help - Desperately need help

  1. #1
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    Desperately need help

    If the demand function for a product is given by price p=1200-150x and the cost function is given by C(x)=900x-4X^3 find the following:

    A. the profit function

    B. the number of units which produce the maximum profit

    C. the maximum profit

    D. the price which produces this maximum profit.
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by sempiternal_athena View Post
    If the demand function for a product is given by price p=1200-150x and the cost function is given by C(x)=900x-4X^3 find the following:

    A. the profit function
    P(x) = x(p(x) - C(x))

    Quote Originally Posted by sempiternal_athena View Post
    B. the number of units which produce the maximum profit
    solve for P'(x) = 0 and solve for x..

    Quote Originally Posted by sempiternal_athena View Post
    C. the maximum profit
    substitute what you found in (B) to P(x)

    Quote Originally Posted by sempiternal_athena View Post
    D. the price which produces this maximum profit.
    substitute what you found in (B) to p(x)
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  3. #3
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    Thank you for your help, can u tell me if this is correct?
    P(x) = x(p(x) - C(x))
    P(x)=x(1200-150x^2-(900x-4X^3 )
    A).P=1200x-150x^2-900x-4x^3= 4x^3-150x^3-300x
    B.)P`=12x^2-300x^2-300= two answers 1.04356 and 23.9564
    C.)1200(1.04356)-150(1.04356^2)-900x(1.04356)-4(1.04356^3)=154
    D.)p(x)=1200-900(1.04356)=260.8
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  4. #4
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by sempiternal_athena View Post
    Thank you for your help, can u tell me if this is correct?
    P(x) = x(p(x) - C(x))
    P(x)=x(1200-150x^2-(900x-4X^3 )
    A).P=1200x-150x^2-900x-4x^3= 4x^3-150x^3-300x (Although this last expression is correct.
    B.)P`=12x^2-300x^2-300= two answers 1.04356 and 23.9564
    take note of the red ones.. try checking it.. it will affect the answers in C and D..
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