linear programming

Chapter Guide. This chapter concentrates on model formulation and computations in
linear programming (LP). It starts with the modeling and graphical solution of a twovariable
problem which, though highly simplified, provides a concrete understanding
of the basic concepts of LP and lays the foundation for the development of the general
simplex algorithm in Chapter 3. To illustrate the use of LP in the real world, applications
are formulated and solved in the areas of urban planning, currency arbitrage, investment,
production planning and inventory control, gasoline blending, manpower
planning, and scheduling. On the computational side, two distinct types of software are
used in this chapter. (1) TaRA, a totally menu-driven and self-documenting tutorial
program, is designed to help you understand the basics of LP through interactive feedback.
(2) Spreadsheet-based Excel Solver and the AMPL modeling language are commercial
packages designed for practical problems.
Imagine that you have a 5-week business commitment between Fayetteville (FYV)
and Denver (DEN). You fly out of Fayetteville on Mondays and return on Wednesdays.
A regular round-trip ticket costs $400, but a 20% discount is granted if the dates
of the ticket span a weekend. A one-way ticket in either direction costs 75% of the regular
price. How should you buy the tickets for the 5-week period?
We can look at the situation as a decision-making problem whose solution requires
answering three questions:
1. What are the decision alternatives?
2. Under what restrictions is the decision made?
3. What is an appropriate objective criterion for evaluating the alternatives?