This is an optimality conditions nonlinear optimization question.

Let the following optimization problem be given: f(:r:) )min, $6132 gl($1,:r2) := 3(m1 1)3 2132 + 2 S 0 92(1715332) := ($1 1)3 +2172 2 S 0 9393131172) 3: 31 S 0 g4($1,$2) := $2 5 0 0,) Plot the feasible region. b) Solve the optimization problem for the following objective functions: (2') f(-'I?1,$2) == ($1 - 1)2 + ($2 - %)2 (ii) f(:cl,x2) := (x1 1)2 + (932 4)2 Regard the objective function on the 'upper boundary' of f. (z'z'z') f(1v1,:v2) := (3:1 $2 + (x2 _ g)2 Do the KKT conditions hold at the optimal point? Hint: In addition illustrate these problems graphically