00:01
In this question, we are given the demand equation and we are asked to find the quantity that will maximize the revenue.
00:07
Recall that the revenue is a product between the price and the quantity.
00:12
So in our case, it's q multiplied by e to the negative 0 .065 q.
00:19
And we need to maximize that function.
00:22
To maximize the function, we need to calculate r prime.
00:26
And our prime by the product rule equals to e to the negative 0 .065.
00:31
Q plus q multiplied by the derivative of e.
00:37
To calculate the derivative of e, we need to differentiate e.
00:42
And the derivative of e is e itself.
00:46
And then we need to multiply that by the derivative of the exponent, which is negative 0 .065.
00:57
We can factor out e to the negative 0 .065 q...