Originally Posted by

**Reskal** The numbers must be positive for both problems and cannot be zero.

For the first problem I set up the two equations

xyz=32000

2xz+2yz+xy=f(x,y,z)

Solved for z=3200/xy

and then set that in the second equation to get

64000/y+64000/x+xy=f(x,y,z)

taking the gradient I get (-64000/x^2+y, -64000/y^2+x)

When I began to do the second derivative test and solved for fxx I realized that my answer would yield a maximum and was stuck there.

(langrange multipliers is not until the next section so I doubt I am supposed to use those, will these start making these problems easier?)

For the second problem

I set the two equations to be x+y+z=100 and xyz=f(x,y,z)

solved for z=100-x-y and subed that into the second equation to get

xy(100-x-y)

took the gradient of that to get

fx=100y-2xy-y^2

fy=100x-x^2-2xy

and got stuck after that.

Thanks all!