Originally Posted by
holly123 find the maximum and minimum values of the function subject to the given contraint.
f(x,y)= 8x+3y
subject to (x-1)^2 + (y+2)^2 = 9
so i took the gradient of each..
(8, 3)
(2x-2, 2y+2)
and to solve for the max and min, we need to use lagrange multipliers. so the gradient of f is equal to the gradient of g times lambda (some constant)
i have the equations
8= lambda(2x-2)
3=lambda(2y+4)
(x-1)^2 + (y+2)^2 =9
how do i solve this system of equations? the answer in the back of the book is kind of crazy...
x= 1 - 24/sqrt 73
y= -2- 9/sqrt 73
lambda= -sqrt 73/6