Question

Let R be the feasible region (convex polygon) 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,

Options

• optimal value must occur at the centroid of the feasible region

• optimal value must occur at a corner point (vertex) of the feasible region

• optimal value must occur at the midpoints of the corner points (vertices) of the feasible region

• None of these

Answer 1

optimal value must occur at a corner point (vertex) of the feasible region

Explanation:

For a linear programming problem, let R be the feasible region (convex polygon) and Z = ax + by be the objective function. When the variables x and y are subject to constraints given by linear inequalities and Z has an optimal value (maximum or lowest), the ideal value must occur at a corner point (vertex) of the feasible region.