Question

1. The shaded area in the following graph represents the feasible region of a linear programming problem whose objective function is to be maximized. x2 (3, 3) (6, 3) (0, 2) (0, 0) (6, 0) x1 Label each of the following statements as "True" or "False", and then justify your answer based on the graphical method. a) If (3, 3) produces a larger value of the objective function than (0, 2) and (6, 3), then (3, 3) must be an optimal solution. ( ) b) If (3, 3) is an optimal solution and multiple optimal solutions exist, then either (0, 2) or (6, 3) must also be an optimal solution. ( )

          1. The shaded area in the following graph represents the feasible region of a linear programming problem whose objective function is to be maximized.

x2
(3, 3)
(6, 3)
(0, 2)
(0, 0)
(6, 0) x1

Label each of the following statements as "True" or "False", and then justify your answer based on the graphical method.

a) If (3, 3) produces a larger value of the objective function than (0, 2) and (6, 3), then (3, 3) must be an optimal solution.
( )

b) If (3, 3) is an optimal solution and multiple optimal solutions exist, then either (0, 2) or (6, 3) must also be an optimal solution.
( )

1. The shaded area in the following graph represents the feasible region of a linear programming problem whose objective function is to be maximized.

x2
(3, 3)
(6, 3)
(0, 2)
(0, 0)
(6, 0) x1

Label each of the following statements as "True" or "False", and then justify your answer based on the graphical method.

a) If (3, 3) produces a larger value of the objective function than (0, 2) and (6, 3), then (3, 3) must be an optimal solution.
( )

b) If (3, 3) is an optimal solution and multiple optimal solutions exist, then either (0, 2) or (6, 3) must also be an optimal solution.
( )

Added by Christopher W.

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