$2$ 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 $2$x$\_(1)+4$x$\_(2)$

Subject to x$\_(1)+$x$\_(2),<=3$

x$\_(1)-4$x$\_(2),>=-8$

$5$x$\_(1)-$x$\_(2),>=-1$

$2$x$\_(1)+$x$\_(2),<=5$

x$\_(1),>=0$

$,$x$\_(2)$

$>=0$

a: Find an example of a different objective function that has a positive coefficient

on x$\_(2),$ but that has x$\_(2)$ equal to zero in the only optimal solution.

IMSE $3005,$ Assignment #$4$

Page $2$

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.