Use Lagrange multipliers to find the indicated extrema of f

Solution

let h=x+y+z-28 g=x-y+z-16 The system is given by grad f=s grad h+t grad g we get yz=s+t xz=s-t xy=s+t so yz=xy y(x-z)=0 x=z x+y+z=28 x-y+z=16 we add them 2(x+z)=44 x+z=22 x=z=11 y=6 So the critical value is (11,6,11) and the maximum at it is 11*6*11=726