00:01
Here we have a situation where we're told the price and we want to maximize the revenue.
00:05
So let's just go ahead and say the revenue is going to be x times the price.
00:09
Well, we know the price is going to be 195 minus 0 .1 x.
00:13
So let's just multiply that by x.
00:15
So that's 195 x minus 0 .1 x squared.
00:18
Now that we know the revenue, all we have to do is take its derivative and set it equal to zero and that will maximize the revenue.
00:25
So we'll take the derivative, r prime, set that equal to 195.
00:29
That's the derivative of 195 x using the power rule.
00:32
Another power rule says we have the 2 times 0 .1, which is 0 .2 x.
00:36
So i'll set that equal to zero.
00:38
I'm going to subtract 195 and divide by negative 0 .2 to get 195 divided by 0 .2, which is x equals 975...