Below is an optimal simplex tableau of a problem with con- straints, and x6, x7, and x8 as the slack variables. N N 1 0 x1 0 1 x2 x1 0 0 x2 x3 0 0 1 0 0 0 x3 0 0 0 1 x4 3 -2 3 4 x5 x6 1 0 -1 2 4 1 2 -1 x7 3 0.5 0 x8 1 -1 -3 1 RHS z* 1 3 2 (a) What is the optimal value z* of the problem? (b) If a new activity x9 with constraint coefficient and an objective coefficient 7 is added to the problem, would the optimal solution be different? (c) How small can the first constraint coefficient b1 be, without violating feasibility? (d). If we add the constraint 2x1-x2 +4x3 2 to the model discussed, would the previous optimal solution still be optimal? If not, find a new optimal solution