Problem 2. (17 marks in total) You are given the following LP problem: max z = 500x +450x2 s.t. 6x +5x2 60 10x +20x2 150 x 8 X1, X2 0 a. (6 marks) Draw the solution space of the problem. b. (4 marks) Find the extreme points of the problem. c. (2 marks) Find an optimal solution to the problem, as well as the optimal value. d. (5 marks) Find the range of optimality for each coefficient of the objective function.