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 asks about the fundamental assumptions and requirements that define a Linear Programming Problem (LPP). An LPP is a mathematical technique for optimizing (maximizing or minimizing) a linear objective function, subject to a set of linear constraints.
Step 2: Detailed Explanation:
Let's review the options based on the definition of an LPP:
1. All the elements of an LPP should be quantifiable. This is a basic requirement. The objective function and constraints must be expressed in terms of numerical values (coefficients, constants). This is the "linearity" and "programmable" aspect. So, this is a requirement.
2. All decision variables should assume non-negative values. This is the non-negativity constraint (\(x_i \ge 0\)), a standard requirement in most LPPs, ensuring that the variables represent real-world quantities like production units, which cannot be negative. So, this is a requirement.
3. There are a finite number of decision variables and a finite number of constraints. This is the finiteness requirement. The problem must be bounded in scope with a specific number of variables to solve for and a specific number of conditions to meet. So, this is a requirement.
4. It deals with optimizing number of objectives more than one. This is not a requirement. A standard LPP is defined by having a single objective function to optimize. Problems that involve optimizing multiple objectives simultaneously are known as multi-objective optimization problems, which is a different field from standard linear programming.
Step 3: Final Answer:
The statement that is NOT a basic requirement of an LPP is that it deals with optimizing more than one objective.