00:01
Hi there, so for this problem, the cost function that we are given for this is 5 ,500 plus 200 times x.
00:09
And the revenue function for this also given that will be minus x squared divided by 2.
00:16
And then this loss 300 times x.
00:25
Okay, so, well, i'm not sure, but as i can see, we'll have a minus in there.
00:33
You can verify that and change it accordingly.
00:37
Right? so, for part a of this problem, we are asked to find the total profit function p of x.
00:44
Now, the profit function is quite easy.
00:46
It's just a revenue minus the cost function.
00:49
So let's do that.
00:50
Let's substitute the expressions in here.
00:52
So, as you can see, that will be this minus this.
00:55
So that will give us minus 500 times x.
00:59
That's the first term.
01:00
And then we will have minus x squared divided by 2.
01:05
This term in here, then this minus this, which will give us minus 5 ,500.
01:11
So that is the expression for the profit.
01:16
Now, for part b of this problem, the question is to find the number of items x for which the total profit is a maximum.
01:22
So we need to derivate this profit expression with respect to x.
01:25
So that will be minus 500 and then this minus x...