Hello!! I need this to be done for me within one hour because I have test in one hour. I need with explanation please and thank you.

Consider the following family of nonlinear programming problems parametriz minx; + (x2 - 1)2 subject to - # +x2 + 1 5 0 and x2 2 0. (1) (a) Show that the linear independence constraint qualification holds at all feasible points for all & # 0. (b) What values of k, would guarantee that a KKT point, when it exists, is a global minimum? (c) Write down the KKT conditions and compute all KKT points for a given k # 0. (d) Based on the set of KKT points found in (c) find out what value would & have to approach so that the corresponding KKT point would approach the optimal solution of the unconstrained version of (1). (e) Consider the following output from GAMS for two values of k: k =4 k = 2 SOLVER STATUS 1 Normal Completion *# SOLVER STATUS 1 Normal Completion ONE MODEL STATUS 7 Feasible Solution NEW MODEL STATUS 2 Locally Optimal HER OBJECTIVE VALUE 5.0000 THE OBJECTIVE VALUE 3.0000 LOWER LEVEL UPPER LOVER LEVEL UPPER MARGINAL ---- SQU 083 -=== EQU C1 -INF -1.000 -1.000 - EQU OBJ 1.000 - EQU CI -INF -1.000 -1.000 -2.000 OBJ COST FUNCTION OBJ COST FUNCTION Ci Constraint 1 CI Constraint 1 LOWER LEVEL UPPER LOVER LEVEL UPPER MARGINAL ---- VAR X1 -INF 2.000 + INF -INE 1.414 mmm= VAR X2 INF - VAR X1 -INF - VAR X2 INF -- VAR Z 5,000 + INF mmm= VAR Z - INF 3.000 (e.1) Comment on the two outputs. (e.2) Are the reported solutions consistent with your analysis in parts (a-d)? Explain. (e.3) What does MARGINAL mean? (e.4) Why is it that no MARGINAL value is reported for * = 4? (e.5) What is the interpretation of MARGINAL when k = 2