The tableau given below corresponds to a maximization problem in decision variables 0(j = 1, 2, ,5): %3D Basic variables Current values X2 X3 X4 X5 x3 4 -1 a1 X4 1 a2 -4 1 X5 b 3 1 (-z) -10 -2 State conditions on all five unknowns a1, a2, a3, band c such that the following statements are true. (a) The current solution is optimal. There are multiple optimal solutions. (b) The problem is unbounded. (c) The problem is infeasible. (d) e current solution is not optimal (assume that b 2 0). Indicate the variable that enters the basis, the variable that leaves the basis, and what the total change in profit would be for one iteration of the simplex method for all values of the unknowns that are not optimal. Question 5 (a) In our discussion of reduction to canonical form, we have replaced variables unconstrained in sign by the difference between two nonnegative variables. This exercise considers an alternative transformation that does not introduce as many new variables, and also a simplex-like procedure for treating free variables directly without any substitutions. For concreteness, suppose that Y1, Y2; and y3 are the only unconstrained variables in a linear program. Substitute for y1, 42, and y3 in the model by: Y = x1 x0 Y2 = x2 xo Y3 = x3 xo with xo 2 0, x 2 0, x2 2 0, and x3 2 0. Show that the models are equivalent before and after these substitutions. b) Apply the simplex method directly with y1, Y2, and y3. When are these variables introduced 4