ABSTRACT
This chapter derives properties of polyhedra, which underly algorithms for linear optimization. It starts with a theorem of the alternative for a system of linear equalities, which is related to Lagrange's method, and then move to theorems for polyhedra. The chapter teaches LP formulation, how to build an LP model that accurately describes the critical elements of a problem. The main steps in model building are: understand and visualize the problem; define index sets and data; define the decision variables; write the objective function as a linear combination of the decision variables; and write the constraints as linear inequalities in the decision variables. Banks that loan money are in the opposite situation. A false negative is a customer who would have repaid a loan but was turned down – a missed opportunity to make a profitable loan, but an important mistake in a world full of loan applicants.
