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Math Help - Marginal Cost/Demand and Cost

  1. #1
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    Marginal Cost/Demand and Cost

    1. The Marginal Cost of a product is modeled by dC/dx = 4/(x+1)^1/2
    When x=15, C=50. Find the Cost function.

    2. The demand and cost functions for a product are given by:
    p=600 -3x
    C=0.3x^2+6x+600
    where p is the price per unit, x is the number of units, and C is the total cost. The profit for producing x units is given by:
    P=xp - C -xt
    where t is the excise tax per unit. Find the maximum profits for excise taxes of t=$5, $10, and $20.

    Help for these two questions would be great! thanks
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  2. #2
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    Quote Originally Posted by Auger View Post
    1. The Marginal Cost of a product is modeled by dC/dx = 4/(x+1)^1/2
    When x=15, C=50. Find the Cost function.

    2. The demand and cost functions for a product are given by:
    p=600 -3x
    C=0.3x^2+6x+600
    where p is the price per unit, x is the number of units, and C is the total cost. The profit for producing x units is given by:
    P=xp - C -xt
    where t is the excise tax per unit. Find the maximum profits for excise taxes of t=$5, $10, and $20.

    Help for these two questions would be great! thanks
    1) Integrate, use extra info to solve for the constant of integration.
    2)Differentiate P and find critical points. Do this three times for t=5,10,20
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  3. #3
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    Thanks. For #1, I did use integration by substitution, making u=x+1, i ended up getting I= 4ln(x+1)^1/2 + C. I sub'd in the c and x values, and got an answer of approx. 55.55, however the answer in the back of the book is C= 8(x+1)^1/2 + 18. What am I doing wrong?
    For #2, I did just that, filling in equation P and finding the derivative, and i got the values: $5 ->-89.24, $10 -> -88.48, and $20 -> -86.97
    I don't know if anyone is willing to see what they get, but my answers just seem off. Thanks
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  4. #4
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    \int \frac{4}{\sqrt{x+1}}dx = \int 4(x+1)^{-\frac{1}{2}}dx

    There won't be any natural logs in the answer. It's a simple power rule situation.
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  5. #5
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    Thanks again but I still don't understand how they got the answer: 8(x+1)^1/2 + 18
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