Introductory Mathematics and Statistics for Islamic Finance, + Website

Chapter 10Linear Programming

Linear programming (LP) is an important field of Islamic finance. LP is basic to understanding economic efficiency, the optimal allocation of resources, and the valuation of these resources. Learning LP allows us to understand how scarce resources ought to be used in the most efficient way and how they ought to be valued. If scarce resources are allocated to sectors where they are wasted, then there is tremendous loss in growth. For instance, cheap money policy forces allocation of resources to wasteful uses and causes inflation and significant loss of real income.

Allocation and valuation of resources are carried out simultaneously in LP. Many corporations in Islamic finance, transportation, oil refining, agriculture, mining, industrial sectors, and utilities rely on LP in managing their investment, production, and distribution activities. LP has a dual form called allocation and valuation of resources; it consists of finding a set of instruments:

• that maximize a linear function subject to linear constraints , .
• Or in dual form, that minimize a linear ...