Question

In an LPP, if the objective function z = ax + by has the same maximum value on two corner points of the feasible region, then the number of points at which z_max oocurs is ______.

Options

• 0

• 2

• finite

• infinite

Answer 1

In an LPP, if the objective function z = ax + by has the same maximum value on two corner points of the feasible region, then the number of points at which z_max oocurs is infinite.

Explanation:

If the objective function z = ax + by has the same maximum value at two corner points of the feasible region, then every point on the line segment joining those two corner points will also give the same maximum value.

Since a line segment contains infinitely many points, the maximum value occurs at infinitely many points.