00:01
To maximize the function ff xy equals x squared plus y squared, subject to the constraint that 2x plus 3y equals 6, we begin by setting up our gradient equation.
00:09
We'd have that 2x must equal 2 times lambda.
00:13
We'd have that 2y must equal 3 times lambda.
00:17
And we have our constraint equation as well, 2x plus 3y equals 6.
00:22
Now i need to be careful.
00:24
My lambda's there looked a little bit like x's.
00:26
So i'll do lambda like this.
00:28
So we have three equations, three unknowns, x, y, and lambda.
00:34
We can first see that from our first equation, we get that x must equal lambda.
00:39
Then from our second equation, we get that y must equal three times lambda over two, which in turn means that it must equal three times x over two.
00:49
Then we can substitute that in to our third equation here...