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: Concept Clarification:
This question concerns the fundamental assumptions and prerequisites that characterize a Linear Programming Problem (LPP). An LPP is a mathematical methodology employed to optimize (maximize or minimize) a linear objective function, subject to a defined set of linear constraints.
Step 2: Detailed Analysis:
Let us examine the provided options in light of the LPP definition:
1. Quantifiable Elements: This is a prerequisite. The objective function and constraints must be expressible using numerical values (coefficients and constants). This aligns with the "linearity" and "programmable" aspects of LPP. Thus, this is a requirement.
2. Non-negative Decision Variables: This refers to the non-negativity constraint (\(x_i \ge 0\)), a standard stipulation in most LPPs. It ensures variables represent tangible quantities, such as production units, which cannot be negative. Therefore, this is a requirement.
3. Finiteness of Variables and Constraints: This is the finiteness requirement. The problem scope must be bounded, with a specific number of variables to solve for and a defined number of conditions to satisfy. Consequently, this is a requirement.
4. Optimization of Multiple Objectives: This is not a requirement. A standard LPP is characterized by the optimization of a single objective function. Problems involving the optimization of more than one objective concurrently are classified as multi-objective optimization problems, a distinct field from standard linear programming.
Step 3: Conclusion:
The statement that is NOT a basic requirement of an LPP is its engagement in optimizing more than one objective.