00:01
Here, we're given the revenue, the marginal revenue, as 1550 minus 8x.
00:07
And we can find the revenue by taking the integral.
00:10
That's 1550x minus 4x squared.
00:13
We're also given the cost, the marginal cost, as 3x plus 1 ,000 to the 1 third.
00:22
So that means the cost is the integral of that.
00:24
We'll take 3x plus 1 ,000 to the 4 thirds by adding 1.
00:28
Then we'll divide by that, but we also have to account for the 3 in the chain rule.
00:32
So we have 4 thirds, or divide by 4, and then let's say plus an arbitrary constant.
00:36
But we're also told that at time 0, we get 18 ,500...