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.

related to an answer for: Let $R$ be the feasible region for a linear programming problem and let $Z = ax + by$ be the objective function. When $Z$ has an optimal value (maximum or minimum), where the variables $x$ and $y$ are subject to constraints described by linear inequalities, this optimal value must occur where in the feasible region?

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