How can you find a maximum for where z is unconstrained. I mean z could be any positive real number or zero right? then .
f(x,y,z)=xyz+z subject to x^2+y^2<6 with x,y,z>(or equal) 0.
Find the 2 solutions and determine the maximiser.
I've found the KT lagrangian and differentiated etc. but now I'm left with those 3 equations and the complementary slackness and can't solve it from there! Please help!