00:01
So the function that we're trying to maximize is f of x y equals 9 x y squared.
00:13
And then our constraint is that x plus y equals 87.
00:20
So our constrained function is x plus y minus 87.
00:27
So we get our the grange multiplier function, which is f of x y minus 87.
00:35
Minus lambda times g of xy.
00:39
So in this case it's 9x y squared minus lambda x, minus lambda y plus 87 lambda.
00:52
Then we get our partial fraction functions.
00:57
So during respect to x is 9 y squared minus lambda equals 0.
01:07
Derivative with respect to y is 18 xy minus lambda equal zero and our derivative with respect to lambda is minus x minus y plus 87 equals zero now from these two equations we get 9 y squared equals lambda and 18 x y equals and now we can set the left -hand side of each of those equations equal to each other.
01:41
So we get 9 y squared minus 18 x y equals 0.
01:48
Factor out of 9 y.
01:50
So 9 y times see we get y minus 2 x equals 0.
02:00
So this gives us two cases.
02:03
That's the case one.
02:06
We have that 9y equals 0...