1. Which of the following mathematical relationships could be found in a linear programming model, and which could not? For the relationships that are unacceptable for linear programs, state why. a. -1A + 2B < 70 b. 2A - 2B = 50 c. 1A - 2 B 2 < 10 d. 3A +2B 15 e. 1A + 1B = 6 f. 2A + 5B + 1AB 25 7. Identify the feasible region for the following set of constraints: 0.5A + 0.25B 30 1A + 5B 250 0.25A + 0.5B 50 A, B 0 10. For the linear program Max 2A + 3B s.t. 1A + 2B < 6 5A + 3B < 15 A, B > 0 find the optimal solution using the graphical solution procedure. What is the value of the objective function at the optimal solution?