Q.1 Linear programming problems are concerned with optimizing what type of functions?
Linear functions
Quadratic functions
Exponential functions
Logarithmic functions
Explanation - Linear programming deals with the optimization (maximization or minimization) of linear objective functions subject to linear constraints.
Correct answer is: Linear functions
Q.2 In linear programming, constraints are expressed as:
Equations only
Inequalities or equations
Exponential expressions
Non-linear functions
Explanation - Constraints in LPP are linear equations or inequalities that restrict the feasible region.
Correct answer is: Inequalities or equations
Q.3 The set of all possible solutions that satisfy the constraints in a linear programming problem is called:
Objective function
Solution space
Feasible region
Constraint zone
Explanation - The feasible region is the region in which all constraints are satisfied simultaneously.
Correct answer is: Feasible region
Q.4 The feasible region of a linear programming problem is always:
Circular
Convex
Concave
Irregular
Explanation - The feasible region formed by linear inequalities is always a convex polygon or polyhedron.
Correct answer is: Convex
Q.5 Which method is commonly used to solve two-variable linear programming problems graphically?
Simplex method
Dual method
Graphical method
Newton-Raphson method
Explanation - For two-variable problems, graphical representation is the easiest method to solve.
Correct answer is: Graphical method
Q.6 The optimal solution to a linear programming problem always lies:
At the midpoint of the feasible region
At a corner (vertex) of the feasible region
Outside the feasible region
On the constraint lines only
Explanation - The fundamental theorem of linear programming states that the optimum value occurs at a vertex of the feasible region.
Correct answer is: At a corner (vertex) of the feasible region
Q.7 The objective function in a linear programming problem can be:
Only maximized
Only minimized
Maximized or minimized
Neither maximized nor minimized
Explanation - Depending on the problem, the objective function may be maximized (profit) or minimized (cost).
Correct answer is: Maximized or minimized
Q.8 In the simplex method, what is introduced to convert inequalities into equalities?
Slack variables
Artificial variables
Surplus variables
All of the above
Explanation - Slack variables, surplus variables, and artificial variables are used to convert inequalities into equalities in different situations.
Correct answer is: All of the above
Q.9 Which of the following is NOT an assumption of linear programming?
Proportionality
Additivity
Certainty
Non-linearity
Explanation - Linear programming assumes proportionality, additivity, and certainty, but not non-linearity.
Correct answer is: Non-linearity
Q.10 If a linear programming problem has multiple optimal solutions, then:
The objective function is unbounded
The objective function has the same value at multiple vertices
The feasible region does not exist
Constraints are inconsistent
Explanation - Multiple optimal solutions occur when the objective function is parallel to a constraint in the feasible region.
Correct answer is: The objective function has the same value at multiple vertices
Q.11 Which of the following terms refers to a situation where the feasible region is unbounded?
Infeasible solution
Unbounded solution
Degenerate solution
Optimal solution
Explanation - An unbounded solution occurs when the feasible region extends infinitely in the direction of optimization.
Correct answer is: Unbounded solution
Q.12 Which of the following is NOT true about feasible regions in LPP?
It can be empty
It is always convex
It always has a finite area
It can be bounded or unbounded
Explanation - Feasible regions may be bounded (finite) or unbounded (infinite).
Correct answer is: It always has a finite area
Q.13 What is the first step in solving a linear programming problem graphically?
Locate the optimal point
Identify objective function
Plot the constraints
Add slack variables
Explanation - The graphical method begins with plotting the linear constraints to form the feasible region.
Correct answer is: Plot the constraints
Q.14 In the simplex method, which table is repeatedly updated to move towards the optimal solution?
Determinant table
Simplex tableau
Constraint table
Matrix form
Explanation - The simplex tableau helps keep track of the iterations in the simplex method.
Correct answer is: Simplex tableau
Q.15 Which variable is introduced in the simplex method for ‘greater than or equal to’ constraints?
Slack variable
Artificial variable
Surplus variable
Decision variable
Explanation - Surplus variables are subtracted from constraints with ≥ inequality.
Correct answer is: Surplus variable
Q.16 Degeneracy in linear programming occurs when:
There is no feasible solution
There are multiple feasible regions
A basic feasible solution has one or more basic variables equal to zero
Objective function is constant
Explanation - Degeneracy means one or more basic variables in the solution take zero values.
Correct answer is: A basic feasible solution has one or more basic variables equal to zero
Q.17 The dual of a minimization problem in linear programming is:
Another minimization problem
A maximization problem
An infeasible problem
Always unbounded
Explanation - By duality, a minimization problem corresponds to a maximization problem and vice versa.
Correct answer is: A maximization problem
Q.18 In linear programming, decision variables represent:
Constraints
Resources
Quantities to be determined
Slack variables
Explanation - Decision variables are the unknowns whose values are determined by solving the LPP.
Correct answer is: Quantities to be determined
Q.19 In the graphical method, if the feasible region is empty, the problem is said to be:
Unbounded
Infeasible
Optimal
Degenerate
Explanation - If no feasible region exists, the problem has no solution and is called infeasible.
Correct answer is: Infeasible
Q.20 Which of the following statements about linear programming is TRUE?
All solutions must be integer values
It can only handle two variables
Constraints must be linear
Objective function must be quadratic
Explanation - Linear programming requires both the objective function and constraints to be linear.
Correct answer is: Constraints must be linear
Q.21 The corner point method involves:
Evaluating objective function at all feasible corner points
Evaluating derivatives of the objective function
Using Newton’s method
Applying simplex tableau directly
Explanation - By the corner point method, the objective function is evaluated at each vertex of the feasible region to find the optimum.
Correct answer is: Evaluating objective function at all feasible corner points
Q.22 An LPP with no feasible region has:
A unique solution
Infinite solutions
No solution
Multiple solutions
Explanation - If there is no feasible region, there cannot be any solution.
Correct answer is: No solution
Q.23 In simplex method, which variable enters the basis first?
Slack variable
Decision variable with largest coefficient in objective function
Artificial variable
Surplus variable
Explanation - In the simplex method, the entering variable is chosen based on the most positive coefficient in the objective function row (for maximization).
Correct answer is: Decision variable with largest coefficient in objective function
Q.24 The shadow price in linear programming refers to:
Cost per unit of decision variable
Marginal value of a resource
Maximum value of the objective function
Surplus value of slack variables
Explanation - Shadow price indicates how much the objective function would change with a unit increase in resource availability.
Correct answer is: Marginal value of a resource
Q.25 Integer linear programming differs from standard linear programming because:
Decision variables must take integer values
Constraints are quadratic
Objective function is exponential
Feasible region is concave
Explanation - In integer linear programming, decision variables are restricted to integers, unlike standard LPP.
Correct answer is: Decision variables must take integer values