Operations research – optimization: The mathematical technique for best allocation of limited resources to maximize or minimize an objective is called

Introduction / Context:
When resources such as materials, labour hours, machine time, or budget are limited, managers seek an optimal allocation that maximizes profit or minimizes cost. Linear programming (LP) is the core operations research method for such problems with linear objectives and constraints.

Given Data / Assumptions:

• An objective function that is linear in decision variables (e.g., maximize profit = c1x1 + c2x2).
• Linear constraints representing resource limits (e.g., a11x1 + a12x2 ≤ b1).
• Non-negativity of decision variables.

Concept / Approach:
LP models define a feasible region (a convex polytope). The optimal solution lies at an extreme point of this region. Algorithms such as the simplex method or interior-point methods efficiently find the optimum in large problems.

Step-by-Step Solution:

Verification / Alternative check:
Sensitivity analysis tests robustness of the solution to changes in coefficients, validating practical implementability.

Why Other Options Are Wrong:

• Value analysis: improves product value by function–cost study, not optimization modeling.
• Network analysis: schedules projects (CPM/PERT), not general resource allocation.
• Queuing theory: analyzes waiting lines rather than solving linear allocation problems.

Common Pitfalls:
Modeling nonlinear realities as linear without justification; forgetting integer requirements that would require integer programming.

Final Answer:
Linear programming