The following tableau represents a specific simplex iteration. All variables are nonnegative.

The tableau is not optimal for either a maximization or a minimization problem. Thus, when a non basic variable enters the solution it can either increase or decrease z or leave it unchanged, depending on the parameters of the entering non basic variable.

(a) Categorize the variables as basic and non basic and provide the current values of all the variables.

(b) Assuming that the problem is of the maximization type, identify the non basic variables that have the potential to improve the value of z. If each such variable enters the basic solution, determine the associated leaving variable, if any, and the associated change in z. Do not use the Gauss-Jordan row operations.

(c) Repeat part (b) assuming that the problem is of the minimization type.

(d) Which non basic variable(s) will not cause a change in the value of Z when selected to enter the solution?

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Basic Solution -5 41 -1 -10 620 3 -2 -3 -- 12 X3 1 1 6. 1. -1 6 -4