GRADED PROBLEMS Problem 1 Consider the following optimization problem. Maximize Z = 9x1 + 7x2 s.t. 5x1 + 3x2 0 a. Use graphical analysis to identify all corner-point solutions for this model. | Label each as feasible or infeasible. b. Calculate the value of the objective function for each of the CPF solutions. Use this information to identify an optimal solution. Problem Consider the LP in Problem 1. a. What type of optimization problem is this? (LP, MIP, IP, etc.) What does this mean about whether or not we can use the simplex method to solve this problem? b. Introduce slack variables to write the functional constraints in augmented form. C. What can we use as an initial BFS for the simplex method? What is the basis for the initial BFS? d. Prove that (0,4,3,2,0) is a BFS for this problem. What is the basis for this solution? Is it an adjacent BFS to the initial BFS in part c.? e. Prove that (3,0,0,0,1) is another BFSs for this problem. What is a basis for this solution? Is it an adjacent BFS to the previous one in part d.? f. What is the corresponding BFS for the CFP optimal solution identified in Problem 1? What is the optimal basis