(a) Find the dual of the following LP. max z=3x1+7x2+5x3 s.t. 1+2+3+81 = 50 2x13x2+3 +82 = 100 21, 22, 23, 81, 820 (b) The optimal basis of the primal problem is BV={x2, x3} and optimal value * = 300. Write CBV, b and compute B-1. (c) Use feasibility condition, i.e., B-b > 0, and show for what range of b the current basis remains optimal (here b = 50). (d) Use part (b) and find the shadow prices for the problem. (e) Consider b changes to 40. Use the shadow prices and find the new objective value.