Suppose three constraints in a linear program are are aT x $>=1,$ bT x $>=1$ and cT x $>=1.$ Consider the

following distinct cases:

$($a$)$ If aT b $>=0,$ does this mean that one of a or b is redundant? If so$,$ explain why. If not, give an

example.

$($b$)$ Suppose a $=2$b$.$ Is one of the constraints redundant in that case?

$($c$)$ Suppose a $+$ b $=$ c$.$ Is one of the three constraints redundant?