Question $5$

Consider the following simplex tableau that is NOT optimal:

where $M$ is a parameter that represents a big number and

$-x_1,x_2$ and $x_3$ are positive decision variables;

$-s_1$ and $s_2$ are slack or surplus variables;

$-a_1$ and $a_2$ are artificial variables; and

$-z$ is an objective function that must be maximised.

Continue with the simplex algorithm until the final simplex tablean is found and deduce

the optimal solution. If the LP problem is infeasible or unbounded, give the reason for

this and$/$or if the LP problem has multiple optimal solutions, deduce the general optimal

solution.

Important note: At each simplex tableau, indicate the entering variable, the leaving

variable and the pivot element clearly.