ABSTRACT
Chapter 3 has developed into a mathematical programming covering techniques and applications in technology to solve linear, integer, and nonlinear optimization problems. Among the problems illustrated are a supply chain operation, a recruiting office analysis, emergency service planning, optimal path to transport hazardous materials, a minimum variance investments, and cable installation. Linear programming (LP) is a method for solving linear problems, which occur very frequently in almost every modern industry. In fact, areas using LP are as diverse as defense, health, transportation, manufacturing, advertising, and telecommunications. The reason for this is that in most situations, the classic economic problem exists—you want to maximize output, but you are competing for limited resources. The linear in LP means that in the case of production, the quantity produced is proportional to the resources used and also the revenue generated. The coefficients are constants and no products of variables are allowed. In order to use this technique the company must identify a number of constraints that will limit the production or transportation of their goods; these may include factors such as labor hours, energy, and raw materials. Each constraint must be quantified in terms of one unit of output, as the problem-solving method relies on the constraints being used. An optimization problem that satisfies the following five properties is said to be a LP problem. Mathematical programming problems by the nature of the many unknowns are very hard to solve by human inspection, but methods have been developed to use the power of computers to do the hard work. We illustrate the use of several technologies to solve the wide array of mathematical programming problems.
