00:01
So for this problem, we're given marginal cost and marginal revenue, which are actually the derivatives of the cost and revenue.
00:08
If we want to find the profit function, that's going to be, first what we can do is subtract the marginal revenue cost.
00:20
So if we have marginal revenue, well, we know that if we want to get marginal the revenue from the marginal revenue, we just take the antiterivative of the marginal revenue.
00:30
And we know that marginal revenue or the revenue is going to start off at zero with zero production.
00:37
So in this case, we end up getting 44x minus five halves x squared.
00:46
And then the cost function is going to be the anti -derivative of the marginal cost.
00:52
And that's going to end up giving us three halves x squared plus 20x plus some constant.
01:03
And we know that at 80 units, so if we plug in 80 right here, we end up getting, so a c of 80 ends up giving us 11 ,400.
01:19
So in that case, we can determine what that's going to be...