Try each question on your own first. Use the Show Answer button only after you have selected your option, then read the explanation and revise the related concept from your chapter notes.
1. Linear programming deals with optimizing a linear function subject to:
A. A set of linear constraints expressed as inequalities or equations
B. Non-linear constraints only
C. No constraints at all
D. Quadratic equations
Answer: A. A set of linear constraints expressed as inequalities or equations
Explanation: Linear programming problems involve maximizing or minimizing a linear objective function under a system of linear constraints.
2. The function to be maximized or minimized in a linear programming problem (LPP) is called the:
A. Objective function
B. Constraint function
C. Feasible function
D. Decision function
Answer: A. Objective function
Explanation: The objective function represents the quantity (such as profit or cost) that the LPP seeks to optimize.
3. The region that satisfies all the constraints of an LPP simultaneously is called the:
A. Feasible region
B. Infeasible region
C. Objective region
D. Bounded region, always
Answer: A. Feasible region
Explanation: Every point within the feasible region represents a solution that meets all the stated constraints.
4. In a linear programming problem, the optimal (maximum or minimum) value of the objective function occurs at:
A. A corner (vertex) point of the feasible region
B. The exact center of the feasible region
C. Any randomly chosen interior point
D. A point strictly outside the feasible region
Answer: A. A corner (vertex) point of the feasible region
Explanation: By the fundamental theorem of linear programming, the optimal value is always attained at one of the vertices of the feasible region.
5. A feasible region that can be completely enclosed within a circle of finite radius is called:
A. Bounded
B. Unbounded
C. Empty
D. Convex only, with no other property implied
Answer: A. Bounded
Explanation: A bounded feasible region has a finite extent, ensuring that both maximum and minimum values of the objective function exist.
6. The variables in an LPP that are restricted to non-negative values are commonly called:
A. Decision variables
B. Objective variables
C. Constraint variables
D. Slack variables only
Answer: A. Decision variables
Explanation: Decision variables represent the quantities to be determined, and they are typically restricted to non-negative real values.
7. The corner point method in linear programming is used to:
A. Find the optimal solution by evaluating the objective function at every vertex of the feasible region
B. Draw the constraint lines only
C. Determine the slope of each constraint
D. Solve associated differential equations
Answer: A. Find the optimal solution by evaluating the objective function at every vertex of the feasible region
Explanation: By comparing the objective function's value at each vertex, the corner point method identifies the overall maximum or minimum.
8. If the feasible region of an LPP turns out to be empty, the problem is said to have:
A. No feasible solution
B. Multiple optimal solutions
C. A single unique solution
D. An unbounded solution
Answer: A. No feasible solution
Explanation: When no point simultaneously satisfies all the given constraints, the linear programming problem has no feasible solution.
9. A linear programming problem involving two variables can typically be solved graphically by:
A. Plotting the constraints and identifying the resulting feasible region
B. Using matrices exclusively
C. Applying derivatives
D. Using integration
Answer: A. Plotting the constraints and identifying the resulting feasible region
Explanation: For two-variable problems, graphing each constraint as a line allows direct visual identification of the feasible region and its corner points.
10. If the feasible region of an LPP is unbounded, the maximum value of the objective function:
A. May or may not exist, and must be verified carefully
B. Always exists without exception
C. Is always equal to zero
D. Always occurs exactly at the origin
Answer: A. May or may not exist, and must be verified carefully
Explanation: In an unbounded feasible region, a finite optimal value is not guaranteed and must be checked using the values of the objective function along the boundary.
11. The constraints in a linear programming problem are typically expressed as:
A. Linear inequalities
B. Quadratic equations
C. Differential equations
D. Trigonometric equations
Answer: A. Linear inequalities
Explanation: Constraints in an LPP take the form of linear inequalities (or occasionally equalities) involving the decision variables.
12. A common real-world application of linear programming involves:
A. Optimizing resource allocation, such as in diet or manufacturing problems
B. Solving pure geometry problems
C. Finding derivatives of arbitrary functions
D. Computing areas under curves
Answer: A. Optimizing resource allocation, such as in diet or manufacturing problems
Explanation: Linear programming is widely applied in operations research to make the best use of limited resources like materials, time, or budget.
This page contains a chapter-wise objective practice set. Try the questions without checking the answer first, then use the explanation to understand the point you missed. The current page contains 12 questions, so you can practise in smaller sets when you are revising.
Quick revision tip
After the practice set, write down the question numbers you missed and revise only those concepts once more. This makes MCQ practice more useful than repeatedly attempting the same questions without reviewing mistakes.
