00:01
We want to, let's see here, we want to find the maximum of this function here, x squared plus 4 times xy, subject to the constraint that x squared times y equals 4 or x squared times y minus 4 equals 0.
00:17
So here's our constraint function.
00:21
Now we can make our augmented function where we take g and set it equal to yf plus lambda times c, our constraint.
00:34
Now we can take partials with respect to x, y, and lambda, and these are pretty easy because these are just polynomials.
00:40
So we get two times quantity x plus 2y plus lambda xy equals 0.
00:47
And we get for partial respect to y, we get x times quantity 4 plus lambda x and that equals zero.
00:56
And then we get partial respect to lambda, of course, we then get c back and that equals so we have three equations and three unknowns...