Class 12 Maths MCQ – Linear Programming

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

a) Objective function
b) Constraints
c) Non-negative variables
d) Quadratic function

Answer:

d) Quadratic function

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:

a) Satisfy all the constraints
b) Maximize the objective function
c) Minimize the objective function
d) Have non-negative coordinates

Answer:

a) Satisfy all the constraints

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:

a) Feasible solution
b) Optimal solution
c) Boundary solution
d) Interior solution

Answer:

a) Feasible solution

Explanation:

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

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

a) Anywhere in the feasible region
b) Only at the center of the feasible region
c) At the boundary of the feasible region
d) Outside the feasible region

Answer:

c) At the boundary of the feasible region

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:

a) The points which don't satisfy any constraint
b) The points where two constraint lines intersect
c) Arbitrary points inside the feasible region
d) The points where three or more constraint lines intersect

Answer:

b) The points where two constraint lines intersect

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:

a) Optimal
b) Infeasible
c) Unbounded
d) Degenerate

Answer:

b) Infeasible

Explanation:

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

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

a) Deciding the production levels for products A and B
b) Choosing between two investment options
c) Designing a new product
d) Allocating resources in a factory

Answer:

c) Designing a new product

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:

a) Any number of variables
b) Two variables
c) Three variables
d) Four variables

Answer:

b) Two variables

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:

a) The highest point in the feasible region
b) The lowest point in the feasible region
c) Any point in the feasible region
d) Outside the feasible region

Answer:

b) The lowest point in the feasible region

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:

a) Solution can take any value
b) No solution exists
c) Solution exists in a confined range
d) Solution can take extremely large values

Answer:

d) Solution can take extremely large values

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:

a) Feasible
b) Basic
c) Optimal
d) Efficient

Answer:

c) Optimal

Explanation:

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

12. A redundant constraint is one which:

a) Changes the feasible region
b) Doesn't affect the feasible region
c) Removes feasible solutions
d) Introduces additional variables

Answer:

b) Doesn't affect the feasible region

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:

a) Another maximization problem
b) A minimization problem
c) A problem without an objective
d) A problem with no constraints

Answer:

b) A minimization problem

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:

a) Always a polygon
b) Always a circle
c) Always a line
d) Not always a polygon

Answer:

d) Not always a polygon

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:

a) Non-negativity constraints
b) Positive constraints
c) Objective constraints
d) Feasible constraints

Answer:

a) Non-negativity constraints

Explanation:

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

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

a) Minimize production
b) Minimize transportation cost
c) Maximize profit
d) Minimize number of transportation modes

Answer:

b) Minimize transportation cost

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:

a) Graphical method for solving LPP
b) Tabular method for solving LPP
c) Method for solving non-linear problems
d) Method for solving quadratic problems

Answer:

b) Tabular method for solving LPP

Explanation:

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

18. A degenerate solution in linear programming implies:

a) No solution
b) A unique solution
c) Multiple solutions
d) A solution, but not feasible

Answer:

c) Multiple solutions

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:

a) Redundant constraint
b) Slack constraint
c) Surplus constraint
d) Artificial constraint

Answer:

a) Redundant constraint

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:

a) The region above the constraint lines
b) The region below the constraint lines
c) The region between the constraint lines
d) The region outside the graph

Answer:

a) The region above the constraint lines

Explanation:

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

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