3. (13 pts) Consider the following simplex tableau for a minimization problem, corresponding to an LP problem in standard form. Note that z-row is multiplied with -1 . a. (2pts) What value should d take? Explain the reason? b. (2 pts) What is the current solution (x1,x2,x3,x4) ? What is the current cost? (You can also write in terms of a,b,c,d). c. (2 pts) State specific values of a, b, c for which the dual LP is infeasible. Explain why the conditions are needed. d. (2 pts) State conditions on a,b,c for this solution to be optimal and the problem to have inultiple optimal solutions. e. (3 pts) If the basis in this tableau is optimal and we want to increase the coefficient of x1 (which is c1) by (c1 becomes c1+), give upper and lower bounds on E so that this basis remains optimal. f. (2 pts) Give specific values of a,b,c,d for which there is a degenerate optimal solution