Q.1 Which of the following is the main objective of a Linear Programming Problem (LPP)?
To find average values
To optimize an objective function
To calculate probabilities
To solve quadratic equations
Explanation - Linear Programming aims to maximize or minimize a linear objective function subject to linear constraints.
Correct answer is: To optimize an objective function
Q.2 In LPP, constraints are usually expressed as:
Quadratic equations
Inequalities
Differential equations
Exponential functions
Explanation - Constraints in LPP are linear inequalities that define the feasible region.
Correct answer is: Inequalities
Q.3 The feasible region of an LPP is always:
Circular
Polygonal
Parabolic
Exponential
Explanation - Since constraints are linear, the feasible region is bounded by straight lines forming a polygonal shape.
Correct answer is: Polygonal
Q.4 What does the objective function in LPP represent?
Resource limits
Optimization goal
Random variables
Statistical averages
Explanation - The objective function specifies what needs to be maximized or minimized, such as profit or cost.
Correct answer is: Optimization goal
Q.5 In LPP, the region that satisfies all the constraints is called:
Optimal solution
Feasible region
Objective zone
Constraint region
Explanation - The feasible region is the set of all possible solutions that satisfy all constraints.
Correct answer is: Feasible region
Q.6 Which method is commonly used to solve a two-variable LPP graphically?
Substitution method
Elimination method
Graphical method
Newton’s method
Explanation - The graphical method involves plotting constraints and finding the feasible region to determine the optimal solution.
Correct answer is: Graphical method
Q.7 The corner point method in LPP is used because:
Optimum solution lies at a corner point
It avoids solving equations
It works only for quadratic problems
It ignores constraints
Explanation - The optimal value of a linear function over a polygonal region occurs at one of its corner points.
Correct answer is: Optimum solution lies at a corner point
Q.8 If the feasible region is unbounded, then:
No solution exists
There may or may not be an optimal solution
Solution is always infinite
Constraints are invalid
Explanation - An unbounded region may still give an optimal solution, but sometimes the objective function is unbounded.
Correct answer is: There may or may not be an optimal solution
Q.9 Which of the following is NOT an assumption of LPP?
Proportionality
Additivity
Divisibility
Non-linearity
Explanation - LPP assumes proportionality, additivity, divisibility, and certainty. Non-linearity is not allowed.
Correct answer is: Non-linearity
Q.10 If an LPP has two or more optimal solutions, it is called:
Degenerate solution
Multiple optimal solution
Infeasible solution
Unbounded solution
Explanation - When more than one corner point gives the same optimal value, the LPP has multiple optimal solutions.
Correct answer is: Multiple optimal solution
Q.11 Which variable represents unused resources in LPP?
Decision variables
Slack variables
Objective variables
Artificial variables
Explanation - Slack variables are added to convert inequalities into equalities and represent unused resources.
Correct answer is: Slack variables
Q.12 The simplex method is:
A graphical method
An iterative method
A probability method
A substitution method
Explanation - The simplex method is an iterative procedure used to solve LPPs with more than two variables.
Correct answer is: An iterative method
Q.13 Which type of LPP solution exists if no point satisfies all constraints?
Feasible solution
Unbounded solution
Infeasible solution
Multiple solution
Explanation - If the constraints do not overlap to form a feasible region, the solution is infeasible.
Correct answer is: Infeasible solution
Q.14 In LPP, decision variables represent:
Resources used
Values to be optimized
Random factors
Uncertainty measures
Explanation - Decision variables are the unknowns that decision makers control to optimize the objective function.
Correct answer is: Values to be optimized
Q.15 Which of the following can be an objective in LPP?
Maximizing profit
Minimizing cost
Efficient resource allocation
All of the above
Explanation - LPP is widely used for maximizing profit, minimizing cost, and efficient resource allocation.
Correct answer is: All of the above
Q.16 An LPP in which all constraints are equations is known as:
Standard form
Slack form
Canonical form
Graphical form
Explanation - In standard form, all constraints are expressed as linear equations with non-negative variables.
Correct answer is: Standard form
Q.17 Which mathematical property of LPP ensures that the feasible region is convex?
Additivity
Proportionality
Linearity
Convexity of inequalities
Explanation - Linear constraints form convex sets, making the feasible region convex.
Correct answer is: Linearity
Q.18 In graphical solution of LPP, how is the optimal point identified?
By midpoint of feasible region
By intersection of diagonals
By evaluating corner points
By trial and error
Explanation - The objective function is evaluated at each corner point to determine the optimal solution.
Correct answer is: By evaluating corner points
Q.19 If an LPP’s feasible region is empty, the problem is:
Bounded
Infeasible
Degenerate
Multiple
Explanation - An empty feasible region means no solution satisfies all constraints, hence infeasible.
Correct answer is: Infeasible
Q.20 Which variable is introduced to convert ≥ type constraints in LPP?
Slack variable
Surplus variable
Artificial variable
Decision variable
Explanation - Surplus variables are subtracted to handle ≥ type constraints in LPP.
Correct answer is: Surplus variable
Q.21 Artificial variables are used in which method?
Graphical method
Simplex method
Two-phase method
Newton’s method
Explanation - Artificial variables are used in two-phase or Big-M method to find initial feasible solution.
Correct answer is: Two-phase method
Q.22 In LPP, if the objective function is parallel to a constraint boundary, then:
Unique solution
No solution
Multiple solutions
Unbounded solution
Explanation - When the objective function is parallel to a constraint, multiple optimal solutions occur.
Correct answer is: Multiple solutions
Q.23 Which of the following is NOT a characteristic of LPP?
Certainty
Additivity
Proportionality
Randomness
Explanation - LPP assumes certainty in parameters, hence randomness is not a characteristic.
Correct answer is: Randomness
Q.24 Degeneracy in LPP refers to:
Multiple optimal solutions
More variables than equations
Basic variable taking value zero
Unbounded solution
Explanation - Degeneracy occurs when a basic variable assumes a zero value in the solution.
Correct answer is: Basic variable taking value zero
Q.25 The dual of a maximization problem is:
Maximization problem
Minimization problem
Unbounded problem
Degenerate problem
Explanation - The dual of a primal maximization LPP is always a minimization problem.
Correct answer is: Minimization problem