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.