Free Linear Programming MCQs with Answers

• A. The restrictions imposed on decision variables
• B. The quantity to be maximized or minimized
• C. The set of values violating every restriction
• D. The list of constants used only in calculations

Explanation: The objective function expresses the goal of the problem, such as maximizing profit or minimizing cost.

• A. It occurs only at the origin of the graph
• B. It gives the largest possible value of the objective
• C. It satisfies every constraint and sign restriction
• D. It contains equal values for all decision variables

Explanation: A feasible solution satisfies all constraints, including non-negativity or other sign restrictions.

• A. At a point outside the feasible region
• B. At the midpoint of every feasible line segment
• C. At the point nearest to the coordinate origin
• D. At an extreme point of the feasible region

Explanation: The fundamental theorem of linear programming states that an optimum occurs at an extreme point when the feasible region is non-empty and…

• A. 8
• B. 9
• C. 10
• D. 12

Explanation: The relevant corner points include (2,2), (1,3), and the axis points. At (2,2), Z equals 3(2) + 2(2) = 10, which is greater than the…

• A. To remove the non-negativity requirement
• B. To change a maximization problem into minimization
• C. To convert the inequality into an equality
• D. To make the objective function nonlinear

Explanation: A non-negative slack variable s converts the constraint into 2x + 3y + s = 12.

• A. x + y ≤ 5 and x + y ≥ 2
• B. x + y ≤ 5 and x + y ≥ 5
• C. x + y ≤ 3 and x + y ≥ 5
• D. x + y ≥ 3 and x + y ≥ 5

Explanation: The two constraints in option C require the same expression to be at most 3 and at least 5 at the same time.

• A. Proportionality
• B. Divisibility
• C. Certainty
• D. Non-negativity

Explanation: Proportionality means that resource use and contribution to the objective change in direct proportion to each activity level.

• A. A maximization problem with equal constraints only
• B. A minimization problem with greater-than-or-equal constraints
• C. A minimization problem with less-than-or-equal constraints
• D. A feasibility problem with no objective function

Explanation: The standard dual of a primal maximization problem with ≤ constraints is a minimization problem with ≥ constraints.

• A. The sensitivity interval
• B. The objective function line
• C. The feasible region
• D. The infeasibility boundary

Explanation: The common area satisfying every constraint and sign restriction is called the feasible region.

• A. At least one basic variable has a zero value
• B. Every decision variable has a positive value
• C. The objective function has no coefficients
• D. The feasible region has no boundary

Explanation: Degeneracy occurs when one or more basic variables are zero in a basic feasible solution.

• A. Add a slack variable to the left side
• B. Subtract a surplus variable from the left side
• C. Multiply both sides by a positive constant
• D. Replace the inequality with a strict equality

Explanation: A surplus variable is subtracted from a greater-than-or-equal constraint to obtain equality.

• A. Has a positive slack value
• B. Holds as a strict inequality
• C. Is satisfied exactly as an equality
• D. Has a zero objective coefficient

Explanation: A binding constraint is satisfied exactly, so its left side equals its right side.

• A. The feasible region contains no points
• B. The feasible region has exactly one corner point
• C. Every constraint passes through the origin
• D. The objective value can increase without limit

Explanation: A maximization problem is unbounded when feasible points allow the objective value to increase indefinitely.

• A. The objective line is parallel to that edge
• B. The objective line is perpendicular to that edge
• C. The feasible region has no corner points
• D. All decision variables are unrestricted

Explanation: An objective line parallel to a boundary edge can produce the same value at every point on that edge.

• A. The variables must have equal values
• B. The variables cannot take negative values
• C. The variables must be whole numbers
• D. The variables must remain below one

Explanation: Non-negativity restricts each decision variable to zero or a positive value.

• A. 15
• B. 16
• C. 17
• D. 18

Explanation: The relevant corner points include (3,2), where Z equals 18, and (1,4), where Z equals 16.

• A. The side containing the origin
• B. Only the vertical axis
• C. Only the horizontal axis
• D. The side opposite the origin

Explanation: The origin gives 0, which does not satisfy 2x + y ≥ 8. Therefore, the feasible half-plane lies on the side opposite the origin, subject to…

• A. The change in the optimal objective value from one extra resource unit
• B. The original cost of the resource
• C. The total unused amount of the resource
• D. The number of variables in the model

Explanation: A shadow price measures the marginal change in the optimal objective value caused by increasing the right-hand side by one unit, within…

• A. Linear programming always has integer coefficients
• B. Linear programming permits fractional decision-variable values
• C. Integer programming has no objective function
• D. Integer programming excludes all constraints

Explanation: Standard linear programming permits fractional values unless additional integrality restrictions are imposed.

• A. 2x + y ≥ 40
• B. x + 2y ≤ 40
• C. 2x + y ≤ 40
• D. 2x - y ≤ 40

Explanation: If x represents cakes and y represents loaves, total labour use is 2x + y.