Let R be the feasible region for a Linear Programming Problem and let z = ax + by be the objective function. If R is bounded, then the objective function z has :

Both maximum and minimum values on R

If the feasible region $R$ of a Linear Programming Problem is bounded, then it is a closed and finite region.

A linear objective function $z=ax+by$ always attains its extreme values on a closed and bounded region.

Hence, $z$ will have both a maximum value and a minimum value on $R$.

final answer: Both maximum and minimum values on $R$