Linear Programming (LP) – application domains LP techniques can be successfully applied to which of the following industries?

Introduction / Context:
Linear Programming is a general optimization framework for maximizing or minimizing a linear objective subject to linear constraints. Its flexibility makes it applicable across many industries.

Given Data / Assumptions:

• Objective functions and constraints are linear.
• Decision variables are non-negative and divisible.
• Resource limits, balances, and policy constraints can be expressed linearly.

Concept / Approach:
LP problems are formulated with decision variables, a linear objective, and sets of linear constraints. Solutions lie at extreme points of the feasible polytope and are computed efficiently via simplex or interior-point algorithms.

Step-by-Step Solution:
Define variables (e.g., product quantities, flows, workforce hours).Write the objective (e.g., maximize profit or minimize cost).Capture constraints (material balances, capacities, regulatory limits).Solve and interpret results, including sensitivity analysis.

Verification / Alternative check:
Back-testing model recommendations against historical data or pilot implementations often demonstrates improved profitability or service levels.

Why Other Options Are Wrong:
LP is not restricted to discrete manufacturing; it is widely used in chemicals, oil refining, logistics, finance, telecommunications, and services.

Common Pitfalls:
Forcing non-linear realities into linear form without caution; omitting key constraints; failing to validate data quality.

Final Answer:
All of the above