The revenue function for a one-product firm is given by the...

The revenue function for a one-product firm is given by the following equation. egin{equation*} R(x) = 300 - frac{225}{x+5} - x end{equation*} Find the value of x that results in maximum revenue. The maximum revenue results when x = oxed{ }.

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00:02 Rx is given as 300 minus 225 x plus 5 minus x to find the maximum value we will find the critical point first and critical points are calculated by equating the first derivative to 0.

00:24 So take the first derivative of a constant is 0 minus 225 is a constant d by d x of 1 .1 .225 is a constant d by d x of 1.

00:35 X plus 5 minus d by d x of x so it would be minus 2 to 5 it is 1 by x plus 5 can be written as x plus 5 to the power minus 1 so d by d x of this would be minus 1 then x plus 5 to the power minus 2 and then d by d x of x 1 so it can be written as minus 1 by x 1 by x 1 by x of x 1.

01:03 So it can be written as minus 1 by plus 5 to the power 2.

01:08 So replace this by this way.

01:11 So it would be minus 1 x plus 5 to the power 2.

01:16 Now d by d x of x is 1.

01:20 Simplify this whole expression, it would be minus minus cancelled out so it would be 2 to 5 by x plus 5 square minus 1.

01:31 Now equate the first derivative to 0.

01:37 Here.

01:38 Our first derivative is 2 to 5 by x plus 5 whole square minus 1 equals to 0.

01:44 Minus 1 goes here and becomes positive.

01:47 X plus 5 equals to 1.

01:51 Then by cross multiplication equals to x plus 5 whole square.

01:57 2 to 5 is square of 15.

02:00 So x plus 5 will come out to be 15.

02:04 So x will come out to be 10...

Question

The revenue function for a one-product firm is given by the following equation. egin{equation} R(x) = 300 - frac{225}{x+5} - x end{equation} Find the value of x that results in maximum revenue. The maximum revenue results when x = oxed{ }.

Question

The revenue function for a one-product firm is given by the following equation. egin{equation*} R(x) = 300 - frac{225}{x+5} - x end{equation*} Find the value of x that results in maximum revenue. The maximum revenue results when x = oxed{ }.

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The revenue function for a one-product firm is given by the following equation. egin{equation} R(x) = 300 - frac{225}{x+5} - x end{equation} Find the value of x that results in maximum revenue. The maximum revenue results when x = oxed{ }.