Question

Which one of the following is not a basic assumption of linear programming?

• A. Linearity
• B. Additivity
• C. Divisibility
• D. Feasibility

Hint:

While solving linear programming problems, ensure that the assumptions of linearity, additivity, and divisibility hold true for the model. If any assumption is violated, the model may need to be reformulated or approximated.

Answer 1

The Correct Option is D

Linear programming relies on several basic assumptions to ensure that the mathematical model is solvable and meaningful. These assumptions include: - Linearity: This assumption states that the objective function and constraints are linear in nature, meaning they can be expressed as linear equations or inequalities. - Additivity: The additivity assumption indicates that the total effect of all factors in the objective function or constraints is the sum of their individual effects. - Divisibility: Linear programming assumes that decision variables can take any value, including fractions, which means they are divisible. This is an idealization; in reality, variables may be constrained to take integer values in some cases, but this assumption holds in continuous LP problems. Feasibility, on the other hand, is not an assumption but a condition. It refers to whether there is a solution that satisfies all constraints. In other words, feasibility is about the existence of a solution rather than a foundational assumption.