# True or false questions for LP and the simplex method

True or false?

(a) Deleting a constraint leaves the feasible region larger.

(b) Adding a constraint leaves the feasible region either unchanged or smaller.

(c) An LP cannot have an unbounded objective function value.

(a) True because when I graphed a random problem, it looked like the feasible region got bigger.

(b) True -Same as (a) but saw it get smaller.

(c) True because it can have an optimal objective function value but probably not an unbounded objective function value.

But I don't understand how all three are true. Help is very much appreciated!!

• What are the reasonings that lead you to those conclusions? – Siong Thye Goh Jul 14 '19 at 14:38
• This should explain it. – cookiemonster Jul 14 '19 at 14:44

$$(A)$$: It can also remains the same. For example for a $$2$$-dimensional problem, if $$0 \le x\le 1$$ and $$0 \le y \le 1$$ and $$x+y \le 2$$. Removing the last constraints doesn't change the feasible set.
$$(B)$$: Let $$D$$ be the initial feasible set and $$D'$$ be the new feasible set with more constraitns, then we have $$D' \subseteq D$$ since any element of $$D'$$ would satisfy the conditions to be in $$D$$.
$$(C)$$: Consider $$\max x$$, subject to $$y = 0$$. Is it bounded?