The following tableau represent a specific simplex iteration. All variable are non negative. The tableau is not optimal for either a maximization or 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 entering non basic variable :

basicX1X2X3X4X5X6X7X8sol

Z0-504-1-1000620

X8030-2-3-15112

X3011310306

X11-1006-4000

a) categories the variables as basic and nonbasic and provide the current values of all variables.

b) assuming that the problem is of the maximization type, identify the nonbasic variables that have potential to improve the value of Z, if each such variable enters the basic solution determine the associated leaving variable. If any, and associated is change in Z. Do not use gauss_jordan row operation.

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

d) which nonbasic variables will not cause a change in the value of Z when

selected to enter the solutions?