00:01
So we're given a cost function.
00:03
We want to know the profit function.
00:06
So we're given p of x, and we know that revenue is going to be p of x times x.
00:18
So in this case, we're going to have 300x minus 0 .02x squared.
00:24
So then profit, which is revenue minus cost, is going to be 300.
00:36
X minus 0 .02x squared minus and then the cost function 200 plus 12x plus 0 .1 x cubed or x squared.
00:51
So that's what the profit function would look like.
00:53
The marginal profit, that's just taking p prime of x.
00:56
So that's going to be 300 minus 0 .04x minus 12 plus 0 .2x.
01:09
And then marginal profit when x equals 10, we just plug 10 in here, making this 300 minus 0 .4 minus 12 plus 2.
01:24
And then we could simplify that.
01:27
Marginal profit is going to tell us the rate at which the profit is increasing or decreasing per unit sold.
01:36
And then we know that the profit will be at a maximum if we set this equal to 0...