00:04
So you already have one function given here for the demand function.
00:10
So quantity equals 3 ,000 minus 125 p.
00:33
So the key point to also notice here is p is given in thousands.
00:45
So you have something you have to be careful with once you're doing computation later.
00:52
So there is also an unknown function that's not asked for in this problem.
00:56
But you'll have to figure it out by yourself.
00:59
So there's the hidden unknown function here.
01:04
So since it's talking about revenue, revenue is given by revenue equals quantity times price.
01:18
So basically revenue is dependent on how many items you're going to sell and the price of the items you're going to sell.
01:25
That's going to give you revenue.
01:28
So it's asking for the quantity to maximize revenue.
01:40
So all of our equations should be in terms of p, uh, q, i mean quantity.
01:53
So right now we have two different equations with three different unknowns.
02:04
So the important thing to note is when you have maximal revenue, at any other points, you can't have more maximum revenue.
02:15
So the shape of the revenue curve would probably look something like this.
02:28
So you can see that the point of maximum revenue occurs here at a certain defined quantity.
02:34
So the derivative of the revenue at that point would be a horizontal line zero.
02:39
Where the maximum revenue occurs, there's no change in revenue with respect to any quantity.
02:46
Because there's no other quantity that can produce that maximal revenue...