All Free Quantitative Methods MCQs with Answers

• 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.

• A. Proportionality of returns
• B. Certainty of coefficients
• C. Additivity of contributions
• D. Divisibility of activities

Explanation: The divisibility assumption permits variables to have non-integer values, such as 2.5 units.

• A. To create an initial basic feasible solution
• B. To increase the objective function value
• C. To remove a non-negativity restriction
• D. To convert a maximization into minimization

Explanation: Artificial variables provide an initial basis when slack or surplus variables cannot do so.

• A. An artificial variable
• B. A slack variable
• C. A surplus variable
• D. A decision variable

Explanation: A surplus variable is subtracted from a greater-than-or-equal constraint, giving 4x + 3y minus s equal to 12.

• A. The variable with the largest basic value
• B. The variable with the smallest right-hand side
• C. The variable with the least positive coefficient
• D. The variable with the most positive reduced cost

Explanation: For the usual maximization tableau, the entering variable is selected from the column with the most positive improving coefficient.

• A. A basic feasible solution lies at a corner of the feasible region
• B. A feasible solution must maximize the objective function
• C. A basic feasible solution violates no non-negativity condition
• D. A feasible solution must contain only integer variables

Explanation: A basic feasible solution satisfies all constraints and is formed by setting suitable non-basic variables to zero, usually placing it at a…

• A. The dual value must equal the primal value
• B. The primal value cannot exceed the dual value
• C. The primal value must exceed the dual value
• D. The two objective values must both be zero

Explanation: Weak duality states that every feasible primal maximization value is less than or equal to every feasible dual minimization value.

• A. The increase in total available resources
• B. The increase possible before feasibility is lost
• C. The increase possible without changing the current optimal basis
• D. The increase in the number of decision variables

Explanation: The allowable increase shows how much an objective coefficient can rise while the current optimal basis remains optimal.

• A. Minimize Z = 2A + B
• B. Maximize Z = 2A + B
• C. Minimize Z = 30A + 20B
• D. Maximize Z = 30A + 20B

Explanation: The objective function contains the profit contribution of each product, so it is 30A + 20B and must be maximized.

• A. 20
• B. 22
• C. 24
• D. 26

Explanation: The two constraint boundaries intersect at x = y = 8/3. This gives Z = 5(8/3) + 4(8/3) = 24, which exceeds the axis-corner values of 20…

• A. A constraint that determines the objective value
• B. A constraint that makes the model infeasible
• C. A constraint that does not restrict the feasible region
• D. A constraint that requires integer decision variables

Explanation: A redundant constraint is already implied by the other constraints and therefore does not reduce the feasible region further.