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Let $R$ be the feasible region for a linear programming problem and let $Z = ax + by$ be the objective function. Say $R$ is unbounded, and a maximum or a minimum value of the objective function exists. If so, where can it exist?
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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.
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Apr 16, 2013
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balaji.thirumalai
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Answer: If it exisits, it must exisit at a corner point of $R$.
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Apr 16, 2013
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balaji.thirumalai
True or False. If two corner points of the feasible region are both optimal solutions of the same type, i.e., both produce the same maximum or minimum, then any point on the line segment joining these two points is also an optimal solution of the same type.
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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.
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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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True or False: If the feasible region for a LPP is unbounded,maximum or minimum of the objective function $Z=ax+by$ may or may not exist
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If the feasible region for a LPP is __________,then the optimal value of the objective function $Z=ax+by$ may or may not exist.
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Fill in the blank. Any point in the feasible region that gives the ____ value (maximum or minimum) of the objective function is called ____ solution.
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True or False: In a LPP, the minimum value of the objective function $Z=ax+by$ is always 0 if origin is one of the corner point of the feasible region.
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True or False: Maximum value of the objective function $Z=ax+by$ in a LPP always occurs at only one corner point of the feasible region.
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