Introduction:
Linear programming is a mathematical technique used to determine the best possible outcome in a given mathematical model with linear relationships. It involves optimizing an objective function while satisfying a set of constraints. The feasible region represents the set of all possible solutions that satisfy these constraints.

Explanation:
In linear programming, a maximum or a minimum may not exist for a problem under certain conditions. Let's analyze these conditions one by one:

1. Bounded feasible region:
If the feasible region is bounded, it means that there are finite boundaries or limits to the values that the decision variables can take. In such cases, a maximum or a minimum always exists because the feasible region is finite. Therefore, option 'A' is incorrect.

2. Nonlinear constraints:
Linear programming deals with linear constraints, which means that the constraints can be represented by linear equations or inequalities. If the constraints are nonlinear, it implies that the relationships between the decision variables are not linear. In such cases, the problem becomes a nonlinear programming problem, and linear programming techniques may not be applicable. Therefore, option 'B' is incorrect.

3. Continuous objective function:
The objective function represents the quantity that needs to be maximized or minimized. In linear programming, the objective function is always assumed to be continuous. A continuous function is one that does not have any abrupt changes or discontinuities. The continuity of the objective function ensures that a maximum or a minimum can be achieved within the feasible region. Therefore, option 'C' is incorrect.

4. Unbounded feasible region:
If the feasible region is unbounded, it means that there are no finite boundaries or limits to the values that the decision variables can take. In such cases, the solution space extends infinitely in one or more directions, and a maximum or a minimum may not exist. This happens when there are no constraints that restrict the decision variables sufficiently to achieve a finite solution. Therefore, option 'D' is correct.

Conclusion:
In summary, a maximum or a minimum may not exist for a linear programming problem if the feasible region is unbounded. This occurs when there are no constraints that limit the decision variables sufficiently to achieve a finite solution.