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Foundational Properties of a Linear Programming Problem in Operations Research

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1. Which property requires that both the objective function and all constraints be expressed as linear equations or inequalities?
A. Additivity B. Linearity C. Divisibility D. Certainty
2. Which of the following objective functions is considered linear?
A. (Z = 4x + 7y) B. (Z = x^2 + 5y) C. (Z = xy + 3) D. (Z = \sqrt{x} + y)
3. The proportionality assumption implies that:
A. Resources may vary randomly. B. Decision variables must be integers. C. The contribution of each variable changes in direct proportion to its value. D. Variables can be multiplied together.
4. Which foundational property states that the total effect of all decision variables is equal to the sum of their individual effects?
A. Divisibility B. Non-negativity C. Additivity D. Certainty
5. A factory produces 2.5 tons of cement per day. Which foundational property allows this fractional production quantity?
A. Linearity B. Additivity C. Divisibility D. Certainty
6. Which assumption states that all coefficients in the model are known and remain constant throughout the analysis?
A. Certainty B. Divisibility C. Proportionality D. Additivity
7. Which mathematical restriction ensures that decision variables cannot have negative values?
A. Integer Restriction B. Positivity Constraint C. Non-negativity Constraint D. Linear Constraint
8. Which of the following situations violates the assumptions of Linear Programming?
A. Profit per unit remains constant. B. A product requires 5 labor hours per unit. C. Profit is proportional to production quantity. D. Total profit depends on the product of two decision variables.
9. A company must decide how many tables and chairs to manufacture to maximize profit while considering labor and material limitations. Assuming all relationships are linear, this problem is most appropriately solved using:
A. Dynamic Programming B. Linear Programming C. Simulation D. Network Analysis
10. Which of the following is NOT one of the foundational properties of a Linear Programming problem?
A. Linearity B. Additivity C. Randomness D. Non-negativity
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