Hi I need an answer for the following:

3 Linear Programming Duality 3-1. [10 marks] An Infeasible Linear Program with Infeasible Dual. Here we prove the existence of a linear program which is infeasible and whose dual is also infeasible. Consider the LP Maximize c1*1 + C2x2 Subject to X1 - X2 5 61 -X1 + X2 S b2 (P2) X1, X2 2 0 for some b1, b2, C1, C2 E R. (a) Find sufficient conditions on by and b2 to guarantee that (P2) is infeasible. Prove that your conditions are sufficient. (b) Write down the dual of (P2). Call this program (D2). Find sufficient conditions on cj and c2 to guarantee that (D2) is infeasible. Prove that your conditions are sufficient. (c) Using your conditions in parts (a) and (b), write down a linear program which is infeasible and whose dual is infeasible. (d) Prove that your conditions in part (a) are necessary for infeasibility. That is, show that if b, and b2 do not satisfy the conditions you defined, then (P2) is feasible