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

 

 

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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 2x1 + 4x2 Subject to x1 + x X1 5x1 2x1 + x1 - - 3 4x2 -8 X2 1 x < > 5 0 x2 > 0 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. 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 2x1 + 4x2 Subject to x1 + x X1 5x1 2x1 + x1 - - 3 4x2 -8 X2 1 x < > 5 0 x2 > 0 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.