Let the feasible region of the linear programming problem with the objective function Z = ax + by is unbounded and let M and m be the maximum and minimum value of Z, respectively. Now, consider the following statements
I. M is the maximum value of Z, if the open half plane determined by ax + by gt M has no point in common with the feasible region. Otherwise, Z has no maximum value.
II. mis the minimum value of Z, if the open half plane determined by ax + by lt m has no point in common with the feasible region. Otherwise, Z has no minimum value. Choose the correct option.

Options

A. Only I is true .
B. Only II is true
C. Both I and II are true
D. Neither I nor II is true

Answer

C

Explanation

In case, the feasible region is unbounded, we have I. Mis the maximum value of Z, if the open half plane determined `ax+ by gt M ` M has no point in common with the feasible region. Otherwise, Z has no maximum value.
II. Similarly, mis the minimum value of Z, if the open half plane determined by `ax+by gt m ` has no point in common with the feasible region. Otherwise, Z has no minimum value.