OPERATIONS RESEARCH 2026 – LINEAR
PROGRAMMING & OPTIMIZATION VERIFIED
PRACTICE GUIDE
Q1. Which of the following best describes a linear programming problem?
A) Optimization of a nonlinear objective function subject to nonlinear constraints
B) Optimization of a quadratic objective function subject to linear constraints
C) Optimization of a linear objective function subject to linear constraints
D) Maximization only of a linear objective function
RATIONALE: LP involves optimizing (maximizing or minimizing) a linear objective function
subject to a set of linear equality or inequality constraints.
Q2. In an LP model, decision variables represent:
A) The constraints of the problem
B) The quantities to be determined
C) The coefficients of the objective function
D) The right-hand side values of constraints
RATIONALE: Decision variables are the unknowns that the decision-maker controls and seeks
to determine optimally.
Q3. Which of the following is NOT a requirement of a linear programming model?
A) An objective function
B) Decision variables
C) At least one nonlinear constraint
D) Non-negativity constraints
RATIONALE: All constraints in LP must be linear. Nonlinear constraints belong to nonlinear
programming.
,Q4. A furniture company produces chairs and tables. Each chair requires 2 hours of labor and
each table requires 4 hours. Total labor available is 100 hours. Which constraint correctly
represents this?
A) 2C + 4T ≥ 100
B) 2C + 4T ≤ 100
C) 4C + 2T ≤ 100
D) C + T ≤ 100
RATIONALE: Each chair uses 2 labor-hours and each table uses 4. Total cannot exceed 100
available hours, so 2C + 4T ≤ 100.
Q5. The non-negativity constraint in LP states that:
A) All coefficients must be positive
B) The objective function value must be positive
C) Decision variables cannot take negative values
D) All RHS values must be non-negative
RATIONALE: Decision variables typically represent physical quantities (units produced, hours
allocated), which cannot be negative.
Q6. A company wants to maximize profit Z = 5x + 4y. This expression is called the:
A) Objective function
B) Constraint
C) Feasibility condition
D) Non-negativity restriction
RATIONALE: The objective function is the mathematical expression that defines what is being
optimized — profit in this case.
Q7. Which of the following is a valid LP objective function?
A) Maximize Z = 3x² + 2y
,B) Maximize Z = xy + 5
C) Maximize Z = 3x + 2y
D) Maximize Z = 3x/y + 2
RATIONALE: LP requires the objective function to be linear (no products, squares, or
divisions of variables).
Q8. The feasible region of an LP problem is:
A) The set of all possible objective function values
B) The set of all points satisfying all constraints simultaneously
C) The optimal solution point
D) The region where the objective function is maximized
RATIONALE: The feasible region contains all combinations of decision variables that satisfy
every constraint, including non-negativity.
Q9. A constraint of the form ax + by ≥ c in a maximization problem is called a:
A) Non-binding constraint
B) Greater-than-or-equal-to (≥) constraint
C) Equality constraint
D) Redundant constraint
RATIONALE: Constraints are classified by their inequality direction. A ≥ constraint means the
LHS must meet or exceed the RHS.
Q10. Which assumption of LP states that output is directly proportional to input?
A) Additivity
B) Divisibility
C) Proportionality
D) Certainty
, RATIONALE: Proportionality means the contribution of each variable to the objective
function and constraints is proportional to its value.
Q11. A bakery produces cakes (C) and bread (B). Profit per cake is $6 and per bread is $4.
Formulate the objective function.
A) Minimize Z = 6C + 4B
B) Maximize Z = 6C + 4B
C) Maximize Z = 4C + 6B
D) Maximize Z = 6C – 4B
RATIONALE: The bakery wants to maximize profit. Profit = $6 per cake × C + $4 per bread ×
B.
Q12. The assumption that the values of decision variables can be fractions is called:
A) Proportionality
B) Divisibility
C) Certainty
D) Additivity
RATIONALE: Divisibility allows decision variables to take any non-negative real value, not
just integers.
Q13. When all parameters of an LP model are known with certainty, the assumption is called:
A) Divisibility
B) Proportionality
C) Certainty
D) Linearity
RATIONALE: The certainty assumption means all coefficients (objective and constraints) are
known constants.
PROGRAMMING & OPTIMIZATION VERIFIED
PRACTICE GUIDE
Q1. Which of the following best describes a linear programming problem?
A) Optimization of a nonlinear objective function subject to nonlinear constraints
B) Optimization of a quadratic objective function subject to linear constraints
C) Optimization of a linear objective function subject to linear constraints
D) Maximization only of a linear objective function
RATIONALE: LP involves optimizing (maximizing or minimizing) a linear objective function
subject to a set of linear equality or inequality constraints.
Q2. In an LP model, decision variables represent:
A) The constraints of the problem
B) The quantities to be determined
C) The coefficients of the objective function
D) The right-hand side values of constraints
RATIONALE: Decision variables are the unknowns that the decision-maker controls and seeks
to determine optimally.
Q3. Which of the following is NOT a requirement of a linear programming model?
A) An objective function
B) Decision variables
C) At least one nonlinear constraint
D) Non-negativity constraints
RATIONALE: All constraints in LP must be linear. Nonlinear constraints belong to nonlinear
programming.
,Q4. A furniture company produces chairs and tables. Each chair requires 2 hours of labor and
each table requires 4 hours. Total labor available is 100 hours. Which constraint correctly
represents this?
A) 2C + 4T ≥ 100
B) 2C + 4T ≤ 100
C) 4C + 2T ≤ 100
D) C + T ≤ 100
RATIONALE: Each chair uses 2 labor-hours and each table uses 4. Total cannot exceed 100
available hours, so 2C + 4T ≤ 100.
Q5. The non-negativity constraint in LP states that:
A) All coefficients must be positive
B) The objective function value must be positive
C) Decision variables cannot take negative values
D) All RHS values must be non-negative
RATIONALE: Decision variables typically represent physical quantities (units produced, hours
allocated), which cannot be negative.
Q6. A company wants to maximize profit Z = 5x + 4y. This expression is called the:
A) Objective function
B) Constraint
C) Feasibility condition
D) Non-negativity restriction
RATIONALE: The objective function is the mathematical expression that defines what is being
optimized — profit in this case.
Q7. Which of the following is a valid LP objective function?
A) Maximize Z = 3x² + 2y
,B) Maximize Z = xy + 5
C) Maximize Z = 3x + 2y
D) Maximize Z = 3x/y + 2
RATIONALE: LP requires the objective function to be linear (no products, squares, or
divisions of variables).
Q8. The feasible region of an LP problem is:
A) The set of all possible objective function values
B) The set of all points satisfying all constraints simultaneously
C) The optimal solution point
D) The region where the objective function is maximized
RATIONALE: The feasible region contains all combinations of decision variables that satisfy
every constraint, including non-negativity.
Q9. A constraint of the form ax + by ≥ c in a maximization problem is called a:
A) Non-binding constraint
B) Greater-than-or-equal-to (≥) constraint
C) Equality constraint
D) Redundant constraint
RATIONALE: Constraints are classified by their inequality direction. A ≥ constraint means the
LHS must meet or exceed the RHS.
Q10. Which assumption of LP states that output is directly proportional to input?
A) Additivity
B) Divisibility
C) Proportionality
D) Certainty
, RATIONALE: Proportionality means the contribution of each variable to the objective
function and constraints is proportional to its value.
Q11. A bakery produces cakes (C) and bread (B). Profit per cake is $6 and per bread is $4.
Formulate the objective function.
A) Minimize Z = 6C + 4B
B) Maximize Z = 6C + 4B
C) Maximize Z = 4C + 6B
D) Maximize Z = 6C – 4B
RATIONALE: The bakery wants to maximize profit. Profit = $6 per cake × C + $4 per bread ×
B.
Q12. The assumption that the values of decision variables can be fractions is called:
A) Proportionality
B) Divisibility
C) Certainty
D) Additivity
RATIONALE: Divisibility allows decision variables to take any non-negative real value, not
just integers.
Q13. When all parameters of an LP model are known with certainty, the assumption is called:
A) Divisibility
B) Proportionality
C) Certainty
D) Linearity
RATIONALE: The certainty assumption means all coefficients (objective and constraints) are
known constants.
