00:01
We're given the demand and cost functions, and we want to maximize profit.
00:04
So our demand is p, which is 100 minus q.
00:08
So we're going to get our revenue function first, which is going to be r of q, and that's going to be our q times 100 minus q.
00:18
Now to get our profit function, we're going to take that revenue minus the cost function, which they give me, and that's going to be, i'm going to go ahead and distribute this, 100q minus q squared, now i've got to subtract that whole cost function, so i'm going to say minus 1 3rd q cubed plus 7q squared, plus, nope, minus 1 11 q and minus 50.
00:44
Now i need to take that derivative.
00:47
That's going to be 100 minus 2q, that's going to be minus q squared plus 14q minus 111, and that would be 0...