This book fills a gap in the linear programming literature, by explaining the steps that are illustrated but not always fully explained in every elementary operations book - the steps that lead from the elementary and intuitive graphical method of solution to the more advanced simplex tableau method. Most of the world, even those technically trained, can get along very well by seeing a few illustrations of simple linear programming problems solved graphically, followed by instruction in the use of computer software for solving real-world problems. But there needs to be a coterie of initiates who understand the process well enough to explain it to others, to know what the pitfalls, ramifications and special cases are, and to provide further developments. I have used an informal narrative style with a number of worked out examples and detailed explanations, to put the topic within reach.