please solve part a only

(25 marks). Consider the following nonlinear optimisation problem. Objective function: f(x) = mitz3 +23 Constraints: (X1 + 12 + 23) = 48 C+2+ 23=24 (a) Write all the KKT equations/inequalities and use them to identify all candidate opti- misers. (b) Use the second-order sufficient conditions to determine if any candidates are strict local maximisers or minimisers. Note: there is a high degree of symmetry in this problem; use it to your advantage. There are 12 candidates, but finding 4 and invoking symmetry will let you find all of them. Cases of variables equal to each other or not will be useful