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.