Q.1 What is the main objective of Linear Programming (LP)?
To find the maximum or minimum value of a linear function
To solve quadratic equations
To graph non-linear equations
To find roots of a polynomial
Explanation - Linear Programming is used to maximize or minimize a linear objective function, subject to linear constraints.
Correct answer is: To find the maximum or minimum value of a linear function
Q.2 Which of the following is NOT a component of a Linear Programming problem?
Objective function
Constraints
Feasible region
Quadratic function
Explanation - LP problems involve linear objective functions and linear constraints, not quadratic functions.
Correct answer is: Quadratic function
Q.3 In LP, the feasible region is:
A single point
The set of all points that satisfy the constraints
The maximum value of the objective function
The minimum value of the objective function
Explanation - The feasible region consists of all solutions that satisfy all constraints of the LP problem.
Correct answer is: The set of all points that satisfy the constraints
Q.4 What does the graphical method of LP involve?
Plotting constraints and identifying the feasible region
Solving differential equations
Using matrices to find determinants
Finding the derivative of a function
Explanation - The graphical method is used for two-variable LP problems to visualize constraints and find the optimal solution.
Correct answer is: Plotting constraints and identifying the feasible region
Q.5 Which condition must the constraints satisfy in an LP problem?
They must be linear inequalities or equations
They must be quadratic
They must be exponential
They must be trigonometric
Explanation - LP constraints must be linear to ensure a convex feasible region for optimization.
Correct answer is: They must be linear inequalities or equations
Q.6 In LP, the solution always occurs at:
A feasible region vertex
The midpoint of constraints
The origin only
Any point inside the feasible region
Explanation - According to the Fundamental Theorem of Linear Programming, the optimum occurs at a corner (vertex) of the feasible region.
Correct answer is: A feasible region vertex
Q.7 Which of the following is an example of an LP problem in business?
Maximizing profit given production constraints
Calculating compound interest
Finding break-even point using quadratic equations
Forecasting stock prices with regression
Explanation - LP is often used in business to maximize profit or minimize cost while satisfying constraints like labor and materials.
Correct answer is: Maximizing profit given production constraints
Q.8 If a constraint line in a two-variable LP problem has a positive slope, what does it mean?
As x increases, y decreases
As x increases, y increases
x and y are independent
It is not a linear constraint
Explanation - A positive slope indicates that both variables increase together along the line.
Correct answer is: As x increases, y increases
Q.9 Slack variables are used in LP to:
Convert inequalities into equations
Solve quadratic equations
Graph non-linear functions
Eliminate the objective function
Explanation - Slack variables are added to less-than-or-equal-to constraints to transform them into equalities for simplex method calculations.
Correct answer is: Convert inequalities into equations
Q.10 Which of the following represents the objective function in LP?
Max Z = 5x + 3y
x + y ≤ 10
2x + 4y ≥ 8
y = 2x + 5
Explanation - The objective function is the linear function we aim to maximize or minimize in LP.
Correct answer is: Max Z = 5x + 3y
Q.11 If an LP problem has no feasible solution, it is called:
Infeasible
Unbounded
Degenerate
Optimal
Explanation - An LP problem is infeasible when no point satisfies all constraints simultaneously.
Correct answer is: Infeasible
Q.12 An LP problem is said to be unbounded if:
The objective function can increase indefinitely
There is no feasible region
All constraints are equalities
There is only one solution
Explanation - Unboundedness occurs when the feasible region allows the objective function to grow without limit.
Correct answer is: The objective function can increase indefinitely
Q.13 Which method is used for solving LP problems with more than two variables?
Simplex method
Graphical method
Differentiation
Matrix inversion
Explanation - The Simplex method is an algebraic technique suitable for LP problems with multiple variables.
Correct answer is: Simplex method
Q.14 In LP, a degenerate solution occurs when:
Two or more constraints intersect at the same vertex
The feasible region is empty
The objective function is non-linear
All variables are zero
Explanation - Degeneracy occurs when a corner point of the feasible region has more than the minimum number of constraints intersecting.
Correct answer is: Two or more constraints intersect at the same vertex
Q.15 Which of these is NOT a typical application of LP?
Transportation problem
Diet problem
Machine scheduling
Solving cubic equations
Explanation - LP is used in optimization problems, not for solving higher-order algebraic equations.
Correct answer is: Solving cubic equations
Q.16 In the graphical method, how do you find the optimal solution?
By evaluating the objective function at all corner points
By calculating derivatives
By integrating the constraints
By averaging the variables
Explanation - The optimum occurs at one of the vertices of the feasible region, which are evaluated in the graphical method.
Correct answer is: By evaluating the objective function at all corner points
Q.17 If the feasible region is a single point, the LP problem is said to be:
Unique solution
Infeasible
Unbounded
Degenerate
Explanation - When the feasible region reduces to a single point, the LP problem has a unique solution at that point.
Correct answer is: Unique solution
Q.18 Which inequality represents a 'less than or equal to' constraint in LP?
2x + 3y ≤ 12
x + y ≥ 10
3x - y = 5
y - x > 7
Explanation - The '≤' symbol denotes a 'less than or equal to' constraint in LP.
Correct answer is: 2x + 3y ≤ 12
Q.19 In LP, the corner point method is used for:
Finding the optimal solution in two-variable problems
Solving non-linear optimization
Integrating the objective function
Calculating matrix determinants
Explanation - The corner point method evaluates the objective function at vertices to determine the maximum or minimum.
Correct answer is: Finding the optimal solution in two-variable problems
Q.20 Which of the following statements is TRUE for LP problems?
The feasible region is always convex
The objective function must be quadratic
Constraints can be non-linear
There can be multiple optimum values in linear functions
Explanation - LP constraints form a convex polygon/polyhedron in the solution space, ensuring any line segment between feasible points is also feasible.
Correct answer is: The feasible region is always convex
Q.21 If an LP problem has two optimal solutions, it means:
The objective function is parallel to one of the constraints
The problem is infeasible
The feasible region is unbounded
The objective function is non-linear
Explanation - When the objective function line is parallel to a constraint line, multiple points along that line segment yield the same optimal value.
Correct answer is: The objective function is parallel to one of the constraints
Q.22 The solution of a linear programming problem must satisfy:
All constraints and optimize the objective function
Only the objective function
Only one constraint
No constraints
Explanation - A feasible solution must satisfy all constraints and the optimal solution maximizes or minimizes the objective function.
Correct answer is: All constraints and optimize the objective function
Q.23 Which LP problem type minimizes cost instead of maximizing profit?
Cost minimization problem
Transportation problem
Assignment problem
Diet problem
Explanation - Some LP problems focus on minimizing costs rather than maximizing profits, commonly used in production and logistics.
Correct answer is: Cost minimization problem