Operations research in business: linear programming (LP) is classically used to solve which categories of decision problems?

Introduction / Context:
Linear programming (LP) optimizes an objective (such as profit or cost) subject to linear constraints. It is a foundational tool in operations research and analytics, widely applied to logistics, manufacturing, finance, and workforce planning. Recognizing canonical LP problem types helps identify opportunities to apply optimization in practice.

Given Data / Assumptions:

• Decision variables combine linearly; constraints and objective are linear functions.
• Resources (capacity, budget, labor) impose linear limits.
• We focus on classic business exemplars.

Concept / Approach:
Two archetypal LP applications are routing/transportation and product mix. Transportation and assignment models determine optimal shipment routes or allocations from sources to destinations at minimum total cost. Product mix models decide how much of each product to produce within capacity, raw material, and demand constraints to maximize profit or contribution. Both map naturally to LP’s structure and are mainstays in textbooks and real-world solutions.

Step-by-Step Solution:

Verification / Alternative check:
Standard LP examples include the transportation problem, assignment problem, and product mix problem—demonstrably “routes and mixes.”

Why Other Options Are Wrong:
They are not recognized LP categories; “rupees and percentages” are units or formats, not problem classes.

Common Pitfalls:
Applying LP when relationships are nonlinear or discrete; neglecting sensitivity analysis to understand how optimal solutions change with parameter shifts.

Final Answer:
routes and mixes