Let R be the feasible region (convex polygon) for a linear programming problem and Z = ax + by be the objective function. Then, which of the following statements is false? A) When Z has an optimal value, where the variables x and y are subject to constraints described by linear inequalities, this optimal value must occur at a corner point (vertex) of the feasible region . B)If R is bounded, then the objective function Z has both a maximum and a minimum value on Rand each of these occurs at a corner point of R . C) If R is unbounded, then a maximum or a minimum value of the objective function may not exist D) If R is unbounded and a maximum or a minimum value of the objective function z exists, it must occur at corner point of R

Options

A. When Z has an optimal value, where the variables x and y are subject to constraints described by linear inequalities, this optimal value must occur at a corner point (vertex) of the feasible region .
B. If R is bounded, then the objective function Z has both a maximum and a minimum value on Rand each of these occurs at a corner point of R .
C. If R is unbounded, then a maximum or a minimum value of the objective function may not exist
D. If R is unbounded and a maxil'TUJm or a minimum value of the objective function z exists, it must occur at corner point of R

Answer

D

Explanation

If the feasible region is unbounded and the maximum or a minimum value of Z exists, it must occur at a corner point of R.