In Exercises 1-4, properties of solutions to a given linear programming problem are specified. Describe in as much detail as possible the solutions to the dual of the given problem. (Hint: You may need to use Theorems 3.5-3.8.) 1. An optimal solution is [0.27 1.83 0.94 0.5 0 0] with objective function value 117.81. 2. An optimal solution to the dual problem is [0 3 15 0 5]T with dual objective function value 125. 3. There are no feasible solutions to the problem. 4. There are solutions to the dual problem with arbitrarily large dual objective function values.