Question #99856

Max(min) f(x,y,z) = x^2+y^2+z^2

Subject to

X+2y+z=30

2x-y-3z= 10

Check for local second order condition

Subject to

X+2y+z=30

2x-y-3z= 10

Check for local second order condition

Expert's answer

Solution:

"60-4y-2z-y-3z=10"

"50-5y-5z=0"

"10-y-z=0"

"y=10-z"

"x=30-2\\times (10-z)-z"

"x=30-20+2z-z"

"f(x;y;z)\\to f(z)"

"f'(z)=6z"

"6z=0; z=0"

With this value, a minimum of function is achieved.

"f(x;y;z)=10^2+10^2+0^2=200"

Answer: 200, minimum

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