00:01
Okay, so we want to find the max profit.
00:04
So with this giving information, we want to find total revenue, which would just be our price times our demand q.
00:15
And then our total cost equation would be wl plus rk.
00:24
So if we simplified this, we should have just be 4q, and we can rewrite this as 2l minus k.
00:38
It should be minus rk.
00:44
No, probably it should be plus k.
00:52
So in this case, our profit function is going to be total revenue minus total cost, which is going to be for q minus 2l minus k.
01:09
So what we want to do is take the profit, equation with respects to l.
01:15
Take the drift of the property equation with respects to l.
01:25
Wait, one more time, sorry.
01:27
We're going to take the right now.
01:41
Yeah, so we have our property equation and we're going to rewrite it for what q is.
01:47
So if you write this as four times five l.
01:55
0 .5 times k to the power of 0 .3 minus 2l minus k.
02:09
All right yeah so now we want to take the derivative of the profit function with respect to l so in this case we're going to end up with taking a derivative here you're bringing the 0 .5 down but then this would be in multiply about 4 so it's technically 20 times 0 .5 so it's just 10 so we have 10 and l negative 0 .5k will be a constant in this case.
02:45
And then we're going to have minus 2.
02:49
So we want to set that equation equal to 0...