By Dr. Saul I. Gass
Interesting, nontechnical creation covers uncomplicated innovations of linear programming and its dating to operations learn; geometric interpretation and challenge fixing, answer options, community difficulties, even more. Appendix deals specified statements of definitions, theorems, and methods, extra computational techniques. in basic terms high-school algebra wanted. Bibliography.
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Extra info for An Illustrated Guide to Linear Programming
What of the future? It is felt that the key to the successful operation, if not the optimization of complex systems, is the development of a computer-oriented information system which reflects the current status of the operational system. The information system must be coupled with appropriate mathematical models and solution techniques (like linear programming), along with heuristic computer procedures which enable the human element—aided by the computer—to investigate and resolve those elements of the problem which defy precise mathematical descriptions.
For the refrigerator problem, the first solution is the minimum solution. To proceed with the development of the mathematical model of the transportation problem—and to simplify the discussion—we shall introduce some necessary mathematical shorthand. , and, in general, xij the unknown number of refrigerators to be shipped from factory i to store j. We enter these notations into the tableau structure as shown in the tableau: It is now a simple matter to develop the form of the mathematical model.
The objective of the housewife is to plan a breakfast menu such that her children obtain at least the specified nutrients at the minimum cost. 2 cents per ounce, we see that the two suggested solutions would cost 38 cents and 84 cents, respectively. The first solution, to eat 10 ounces of Krunchies, contains 1 milligram of thiamine, 10 milligrams of niacin, and 1100 calories; while the second solution, to eat 20 ounces of Crispies, contains 5 milligrams of thiamine, 5 milligrams of niacin, and 2400 calories.