finding the maximum/minimum with Lagrange multipliers

**adirh** · March 20th 2010, 01:24 AM

hi i need help with finding optimum maximum/minimum of this function:

subject to these constraints:

i've got this far:

now, if 0=0 that means that there are infinite number of solutions, i think its not logical and i've probably had a calculus error...
plz help

**Opalg** · March 20th 2010, 04:32 AM

I think you have this more or less correct. If you arrive at the equation 0=0 it does not mean that there is an infinite number of solutions, it just means that you are going round in circles and deriving an equation that is identically true.

The solutions are $(1)\ x=y=\pm\sqrt{18},\ z=\pm2\sqrt{18}$ and $(2)\ x=-y=\pm\sqrt{18},\ z=0$ .

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