00:01
Hi there, so for this problem we are given the following revenue function, so the revenue function for this is 60 times x and then this minus 0 .1 times x squared, okay, and then the cost function for this is equal to 5 times x and then this plus 15.
00:21
So with that said, the question for this is in your, we need to obtain the profit and the units that must be sold to obtain that profit, okay? remember that x is in units and the rest are in dollars.
00:38
So first, let's determine the profit function.
00:40
The profit function is the revenue minus the cost, so let's substitute the expressions that we are given for this, this is the revenue minus the cost, so we need to change all of the signs for the cost, so that will be minus 5 times x minus 15.
00:56
Now we simplify it in here, we will have 10, we can simplify this with this, so that will give us 55 times x, then this minus 0 .1 times x squared minus 15.
01:10
Once we have this, what we need to do to maximize this is to derive this with respect to x, so that will be 55 minus 0 .2 times x and then we set this equal to 0...