Consider a two-variable linear programming problem whose CPF solutions are (0,0),(6,0), (6,3),(3,3), and (0,2). (a) Graph the feasible region and identify all the constraints for the model. (See Prob. 3.2-2 for a graph of the feasible region.) (b) For each pair of adjacent CPF solutions, give an example of an objective function such that all the points on the line segment between these two corner points are multiple optimal solutions. (c) Now suppose that the objective function is Z=x1+2x2. Use the graphical method to find all the optimal solutions. (d) For the objective function Z=x1+3x2, work through the simplex method step by step to find all the optimal BF solutions. Then write an algebraic expression that identifies all the optimal solutions (Hint: think about linear combination)