00:01
Hi there, so for this problem we are told to suppose that the relationship between the test rate t on important shoes and the total sales, so the total sales for this is equal to 8 minus 21 times the third root of t.
00:16
Now remember that we can write the third root of this as just t elevated to 1 divided by 3.
00:23
So we can write that as 8 minus 21 times t elevated to 1 divided by 3.
00:29
Now once we have this, we need to find the rate, the test rate t that maximizes the revenue for the government.
00:38
So to obtain the revenue in terms of t that will be then t times s.
00:45
So we do this product in here, so we will obtain 8 times t, then this minus 21, and then we will have 1 divided by 3, and then this plus 1.
01:00
So that will give us 4 divided by 3.
01:13
So that will give us t elevated to 4 divided by 3.
01:16
Now we want to maximize this function, so we derivate this function with respect to t.
01:22
So that will be then 8 minus, then we take down the 4 divided by 3, and this time times t minus 1...