## 1. Which of the following is NOT a requirement for a linear programming problem?

### Answer:

### Explanation:

Linear programming deals with linear relationships. Quadratic functions are not linear.

## 2. The feasible region for a system of constraints is the set of all points that:

### Answer:

### Explanation:

The feasible region is defined by the set of points that adhere to all given constraints.

## 3. In a linear programming problem, a solution that satisfies all the constraints is called:

### Answer:

### Explanation:

A solution that adheres to all constraints is termed as feasible.

## 4. The optimal solution to a linear programming problem can be found:

### Answer:

### Explanation:

The best or optimal solution always lies on the edge or boundary of the feasible region.

## 5. The corner points of the feasible region are:

### Answer:

### Explanation:

Corner points are formed by the intersections of the boundary lines, typically two constraints.

## 6. If a linear programming problem has no solution, it is said to be:

### Answer:

### Explanation:

When no solution exists, the problem is termed as infeasible.

## 7. In which of the following situations is linear programming NOT useful?

### Answer:

### Explanation:

Designing is a creative process, whereas linear programming is for optimization problems.

## 8. The graphical solution method can be applied to linear programming problems with:

### Answer:

### Explanation:

Graphical methods are best suited for problems with two variables as they can be easily visualized on a two-dimensional plane.

## 9. If a problem involves minimizing the objective function, the optimal solution will be:

### Answer:

### Explanation:

To minimize, one would look for the smallest value of the objective function within the feasible region.

## 10. Unbounded solution in linear programming implies:

### Answer:

### Explanation:

An unbounded solution suggests that the objective function can take on infinitely large positive or negative values.

## 11. If all resources are fully utilized without any wastage, then such a solution is:

### Answer:

### Explanation:

Optimal solutions utilize resources to their fullest potential to achieve the desired objective.

## 12. A redundant constraint is one which:

### Answer:

### Explanation:

Redundant constraints do not change or affect the shape, size, or position of the feasible region.

## 13. The dual of a maximization linear programming problem is:

### Answer:

### Explanation:

The dual of a maximization problem in linear programming is always a minimization problem.

## 14. The solution space of a system of linear inequalities is:

### Answer:

### Explanation:

The solution space can be any shape depending on the inequalities, not necessarily a polygon.

## 15. The constraints x ≥ 0 and y ≥ 0 are known as:

### Answer:

### Explanation:

These constraints ensure that the solutions for x and y are non-negative.

## 16. In a transportation problem, the objective is to:

### Answer:

### Explanation:

In a transportation problem, the main goal is to determine the most cost-effective way to transport goods.

## 17. The Simplex method is a:

### Answer:

### Explanation:

The Simplex method is a systematic procedure used to solve linear programming problems.

## 18. A degenerate solution in linear programming implies:

### Answer:

### Explanation:

Degeneracy occurs when we get the same optimal value of the objective function with two or more different sets of values for the decision variables.

## 19. A constraint which is not essential to form the feasible region, but is included in the problem is called:

### Answer:

### Explanation:

A redundant constraint doesn’t affect the feasible region.

## 20. The feasible solution space for a set of 'greater than or equal to' type constraints is:

### Answer:

### Explanation:

'Greater than or equal to' constraints encompass the areas above their respective lines.