Question

max -xlog x-ylog y-zlog z
2 2 2
subject to x>=0,y>=0,z>=0,x+y+z=1 and x-z=0
a) verify that the gradients form a linearly independent set for all combinations of simultaneously binding constraints, except at the point (0,1,0). Thus the nondegenerate constraint qualification holds over the entire set except at (0,1,0). How should you deal with the point (0,1,0) in order to solve the maximization problem?

b) Explicitly state the necessary conditions for the optimal points of this problem in terms of x,y,z,u1,u2,lambda1, lambda2, lambda3.

Answer 1

Can you rewrite it with TeX?