Question

Which of the following is NOT a basic requirement of the linear programming problem (LPP)?

• A. All the elements of an LPP should be quantifiable.
• B. All decision variables should assume non-negative values.
• C. There are a finite number of decision variables and a finite number of constraints.
• D. It deals with optimizing number of objectives more than one.

Hint:

Remember the core components of an LPP: (1) a single linear objective function, (2) a set of linear constraints, and (3) non-negativity constraints for the decision variables. Any statement contradicting these core components is incorrect.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This question pertains to the foundational assumptions and prerequisites that characterize a Linear Programming Problem (LPP). An LPP is a mathematical methodology employed for optimizing (maximizing or minimizing) a linear objective function, under a set of linear constraints.
Step 2: Detailed Explanation:
Let us examine the options in light of the LPP definition:
1. All components of an LPP must be quantifiable. This is a fundamental prerequisite. The objective function and constraints must be articulated using numerical values (coefficients, constants). This aligns with the "linearity" and "programmable" aspects. Therefore, this is a requirement.
2. All decision variables must take non-negative values. This refers to the non-negativity constraint (\(x_i \ge 0\)), which is a standard requirement in most LPPs. It ensures that variables represent real-world quantities, such as production units, which cannot be negative. Thus, this is a requirement.
3. There must be a finite quantity of decision variables and a finite quantity of constraints. This is the finiteness prerequisite. The problem scope must be limited, with a specific number of variables to be solved for and a specific number of conditions to be met. Consequently, this is a requirement.
4. It involves optimizing multiple objectives simultaneously. This is not a requirement. A standard LPP is defined by the optimization of a single objective function. Problems that necessitate optimizing several objectives concurrently are classified as multi-objective optimization problems, which constitute a distinct domain from standard linear programming.
Step 3: Final Answer:
The statement that is NOT a fundamental requirement of an LPP is that it involves optimizing more than one objective.