Optimization Techniques (MCA555) – Unit 2: Linear Programming (LP)
Based on MCA Semester III Syllabus --- Introduction to Linear Programming (LP) Linear Programming (LP) is a mathematical technique used to obtain the best possible solution (maximum profit or minimum cost) under given constraints. LP is one of the most widely used optimization techniques in business, engineering, transportation, and manufacturing. --- Definition of Linear Programming Linear Programming is a method of optimizing a linear objective function subject to a set of linear constraints. General Form: Maximize or Minimize Z = c₁x₁ + c₂x₂ + ... + cₙxₙ Subject to: a₁₁x₁ + a₁₂x₂ ≤ b₁ a₂₁x₁ + a₂₂x₂ ≤ b₂ x₁, x₂ ≥ 0 --- Components of Linear Programming Every LP problem consists of: 1. Decision Variables Unknown quantities to determine. Example: x = Number of Chairs y = Number of Tables --- 2. Objective Function Represents the goal. Example: Maximize Z = 50x + 40y --- 3. Constraints Restrictions on resources. Example: 2x + y ≤ 100 x + 3y ≤ 120 --- 4. Non-Negativity Constrai...