Free Linear Programming MCQs with Answers
30 Linear Programming MCQs from Quantitative Methods, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Linear programming models the maximum or minimum of an objective function subject to linear constraints. Questions involve translating word conditions into inequalities, drawing the feasible region, identifying corner points and evaluating the objective function, including cases involving non-negativity restrictions and redundant constraints.
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30 questions · page 2 of 2
- 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.
Correct answer: Divisibility of activities- 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.
Correct answer: To create an initial basic feasible solution- 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.
Correct answer: A surplus variable- 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.
Correct answer: The variable with the most positive reduced cost- 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…
Correct answer: A basic feasible solution lies at a corner of the feasible region- 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.
Correct answer: The primal value cannot exceed the dual 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.
Correct answer: The increase possible without changing the current optimal basis- 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.
Correct answer: Maximize Z = 30A + 20B- 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…
Correct answer: 24- 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.
Correct answer: A constraint that does not restrict the feasible region