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!