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Math Help - Total revenue from

  1. #1
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    Total revenue from

    Assume the total revenue from the sale of X items given by R9x) = In (8x+1),
    while the total cos to produce x items is C(x)=x/5. Find the approxiamate number of items that should be manufactured so that profit, R (x) - C(x) is maximum.

    Thank You all.
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  2. #2
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    Quote Originally Posted by ArmiAldi View Post
    Assume the total revenue from the sale of X items given by R9x) = In (8x+1),
    while the total cos to produce x items is C(x)=x/5. Find the approxiamate number of items that should be manufactured so that profit, R (x) - C(x) is maximum.

    Thank You all.
    Differentiate the function P(x) = R(x) - C(x) = \ln (8x + 1) - \frac{x}{5} with respect to x. (You know how to differentiate this, right?)

    Put that derivative equal to zero to find the x-coordinate of the stationary point. Test the nature of this solution to prove that this stationary point is a maximum turning point.

    Then the value of x found is the answer to the question.
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    Quote Originally Posted by mr fantastic View Post
    Differentiate the function P(x) = R(x) - C(x) = \ln (8x + 1) - \frac{x}{5} with respect to x. (You know how to differentiate this, right?)

    Put that derivative equal to zero to find the x-coordinate of the stationary point. Test the nature of this solution to prove that this stationary point is a maximum turning point.

    Then the value of x found is the answer to the question.
    \frac{dP}{dx} = \frac{8}{8x+1} - \frac{1}{5}.

    \frac{dP}{dx} = 0 \Rightarrow 0 = \frac{8}{8x+1} - \frac{1}{5} \Rightarrow \frac{8}{8x+1} = \frac{1}{5} \Rightarrow 40 = 8x + 1 \Rightarrow ......

    The sign test shows that the value of x corresponds to a maximum turning point.
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