00:01
So here we're talking about a firm optimizing its production.
00:03
We are given a production function of 8x1 to the half plus 8x2 to the half.
00:12
We know that the price of 1 is equal to 1, the price of 2 is equal to 3, and the price of output is equal to 6.
00:22
So i want to set up a profit function, right? profit is equal to revenue minus costs.
00:31
And that profit function is going to be six times the output.
00:35
Because every unit of output you get, you can sell for six, but you have to pay the x1 minus 3x2, right? you are paying $1 for every unit of x1 and $3 for every unit of x2.
00:51
So if i substitute this in, we get 48 x1 to the half plus 48 x2 to the half minus x1 minus 3x2.
01:03
We're now going to differentiate, right? you need to differentiate to get the point where the local maximum, right, where the line is curved.
01:13
If you think of a curved line, the maximum is got to be where the slope is equal to zero.
01:19
Now, we're going to do that...