00:01
Okay, we want to find three positive numbers whose sum is 90 and whose product is maximum.
00:06
So the function we're trying to maximize is a function of three variables.
00:16
And then our constraint is that their sum is 90.
00:21
So constraint, oh, and they're positive.
00:24
So x plus y, since 90, and then x, y, and z are greater than zero.
00:34
So our constraint function is x plus y plus z minus 90.
00:46
And then our garage multiplier function is a function of four variables, half of x, y, z minus lambda times g of x, y, z.
01:00
So in our case, we get x, y, z minus lambda x, minus lambda, lambda, z, plus, 90 lambda...