00:01
So here we are talking about profit, right? and profit is, of course, revenue minus costs.
00:08
So we're given functions for revenue and costs.
00:11
Total revenue is 60 minus q minus q squared.
00:15
This is my revenue function, assuming that it copies correctly.
00:20
And total costs are given as one half q squared plus 30 q plus 30.
00:28
Right? that's total.
00:30
Revenue and total cost, at least from the way it's given in this problem.
00:35
So now what we want to do is take the derivative of profit with respect to quantity.
00:42
And the idea is that if you think of revenue as looking like this, the maximum revenue is going to be where the slope is equal to zero, right? this point is the max, right? so the derivative is taking the slope function, and then we're going to set the derivative equal to zero to find out where we're at the top of that hill.
01:03
So the derivative here with respect to q is equal to 60 goes to zero, minus q is minus 1, minus 2q.
01:11
Be careful with the signs.
01:13
We have minus q minus 30.
01:15
And you notice here we have a problem, right? everything is negative.
01:22
Everything is completely negative, right? so if you try to solve this, you would get 3q is equal to minus 31, and you would have, blah, right? nothing is going wrong.
01:34
So my suspicion is that these revenue and cost functions are not being, you know, calculated correctly in some sense...