Consider the following convex programming problem. Maximize f(x)=10x1-2x1^2-x1^3+8x2-x2^2 subject to x1+x2=2 and x1=0, x2=0 A.

Consider the following convex programming problem.

Maximize f(x)=10x1-2x1^2-x1^3+8x2-x2^2

subject to x1+x2<=2 and

x1>=0, x2>=0

A. Use the KKT conditions to demonstrate that (x1, x2)=(1,1) is NOT an optimal solution.

B. Use the KKT conditions to derive an optimal solution.