2 This problem asks some more questions about the following linear program, which you first saw...

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2 This problem asks some more questions about the following linear program, which you first saw in the previous assignment. Variables may take fractional values. Maximize Subject to 2x1 + 4x2 x1 + x2 < 3 x1 5x1 2x1 X1 - 4x2 -8 X2-1 x2 x2 500 IMSE 500, Assignment #4 Page 2 a: Find an example of a different objective function that has a positive coefficient on x2, but that has x2 equal to zero in the only optimal solution. b: Find an example of a different objective function for which there is more than one optimal solution. c: Give an example of a constraint that, when added to the constraints already given, leaves the feasible region the same as before. d: Give an example of a constraint that, when added to the constraints already given, causes the linear program to have no feasible solutions. 2 This problem asks some more questions about the following linear program, which you first saw in the previous assignment. Variables may take fractional values. Maximize Subject to 2x1 + 4x2 x1 + x2 < 3 x1 5x1 2x1 X1 - 4x2 -8 X2-1 x2 x2 500 IMSE 500, Assignment #4 Page 2 a: Find an example of a different objective function that has a positive coefficient on x2, but that has x2 equal to zero in the only optimal solution. b: Find an example of a different objective function for which there is more than one optimal solution. c: Give an example of a constraint that, when added to the constraints already given, leaves the feasible region the same as before. d: Give an example of a constraint that, when added to the constraints already given, causes the linear program to have no feasible solutions.