# Question: Consider a two variable linear programming problem whose CPF solutions are

Consider a two-variable linear programming problem whose CPF solutions are (0, 0), (6, 0), (6, 3), (3, 3), and (0, 2). (See Prob. 3.2-2 for a graph of the feasible region.)

(a) Use the graph of the feasible region to identify all the constraints for the model.

(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 in part (c), 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.

(a) Use the graph of the feasible region to identify all the constraints for the model.

(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 in part (c), 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.

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