\f10. For the linear program Max 2A + 3B s.t. 1A + 2B = 6 5A + 3B = 15 A, B 20 find the optimal solution using the graphical solution procedure. What is the value of the objective function at the optimal solution? 11. Solve the following linear program using the graphical solution procedure: Max 5A + 5B S.t. 1A = 100 1B = 80 2A + 4B = 400 A, B 20 12. Consider the following linear programming problem: Max 3A + 3B s.t. 2A + 4B = 12 6A + 4B = 24 A, B =0 a. Find the optimal solution using the graphical solution procedure. b. If the objective function is changed to 2A + 6B, what will the optimal solution be? c. How many extreme points are there? What are the values of A and B at each extreme point?6. Three objective functions for linear programming problems are 7A + 10B, 6A + 4B, .Ftest and -4A + 7B. Show the graph of each for objective function values equal to 420. 7. Identify the feasible region for the following set of constraints: Ftest 0.5A + 0.25B = 30 1A + 5B = 250 0.25A + 0.5B = 50 A, B 20 8. Identify the feasible region for the following set of constraints: 2A - 1B =0 -1A + 1.5B = 200 A, B 20 9. Identify the feasible region for the following set of constraints: 3A - 2B 2 0 2A - 1B = 200 1A = 150 A, B 20 .Ftest 10. For the linear program Max 2A + 3B s.t. 1A + 2B = 6 5A + 3B = 15 A, B 204. Show a separate graph of the constraint lines and the solutions that satisfy each of the following constraints: a. 3A - 4B = 60 b. -6A + 5B = 60 C. 5A - 2B = 0