Question

Objective function and constraints are part of

• A. Linear programming
• B. Fourier series
• C. Vector algebra
• D. Probability

Hint:

Associate keywords with topics. For Linear Programming, the key phrases are "optimization," "maximize/minimize," "objective function," and "constraints." This helps in quickly identifying the correct answer in such definitional questions.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The question asks to identify the mathematical field that involves an "objective function" and "constraints". This requires knowledge of the fundamental components of different mathematical concepts.

Step 2: Detailed Explanation:
Let's analyze the components of each option:

• Linear Programming: Linear Programming is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model whose requirements are represented by linear relationships. It is fundamentally composed of:
• An Objective Function: A linear function that is to be maximized or minimized (e.g., \(Z = ax + by\)).

• Constraints: A set of linear inequalities or equations that represent the limitations or restrictions on the decision variables (e.g., \(x + y \le 100\), \(x \ge 0\)).
This perfectly matches the terms in the question.

• Fourier Series: This is a way to represent a periodic function as a sum of simple sine and cosine functions. It does not involve objective functions or constraints in the same way as optimization problems.

• Vector Algebra: This deals with the manipulation of vectors (quantities with both magnitude and direction). It involves operations like addition, subtraction, dot product, and cross product.

• Probability: This is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. It deals with sample spaces, events, and probability distributions.

Step 3: Final Answer:
The terms "objective function" and "constraints" are the core components of a Linear Programming Problem (LPP).