The following tableau represents a specific simplex iteration. All variables are non-negative. X1 X2 X3 X4 X5 X6 X7 X8 Solution Z 0 -5 0 4 -1 -10 0 0 620 X8 0 3 X3 0 X1 1 1 -1 10 23 -3 -1 5 1 12 1 0 3 0 6 0 0 6 4 0 0 0 a) Categorize the variables as basic and non-basic, and provide the current values of all the variables. b) Assuming that the problem is maximization, identify all the variables that will improve the value of Z. If each such variable enters the basis, determine the associated leaving variable (if any) and the associated changes in z without using any Gauss-Jordan operations. c) Repeat the above process if the simplex table is an iteration for minimization (remember in this case Z should reduce). d) Which non-basic variable(s) will not cause a change in the value of z, when selected to enter (for maximization or minimization)?