Problem 4 (20 pts). Use linear program duality to show that exactly one of the following systems has a solution:
1. Ax < 6
2. yTA = 0, bTy < 0, y > 0. This is another example of using linear optimization duality to understand when a linear optimization problem has a feasible solution. HINT: You may want to first show that both systems cannot have solutions at the same time. Then show that if the second one is infeasible, the first one must be feasible.