Let $R$ be the feasible region for a linear programming problem and let $Z = ax + by$ be the objective function. Say the objective function Z has both a maximum and a minimum value on R and each of these occurs at a corner point (vertex) of R. For this to be true, R must be unbounded. True or False.

Answer: False. R must be bounded. If R is unbounded, then a maximum or a minimum value of the objective function may not exist. However, if it exists, it must occur at a corner point of R.