By Dr. Saul I. Gass
Exciting, nontechnical creation covers easy recommendations of linear programming and its dating to operations study; geometric interpretation and challenge fixing, resolution recommendations, community difficulties, even more. Appendix bargains targeted statements of definitions, theorems, and methods, extra computational techniques. in simple terms high-school algebra wanted. Bibliography.
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Additional info for An Illustrated Guide to Linear Programming
In making this statement, I assume we have been able to capture the real-life situation—that is, the actual problem we wish to solve—by proper definition and manipulation of variables and constraints. In many instances, in fact, in most instances, our ability to portray the true, the genuine, the problem, is open to question. As in all other areas of human endeavor, we find that compromises, resourcefulness, and a little finagling help to obtain a better understanding of the process in question and, we hope, lead to a mathematical model which yields an improved solution that can be put to work.
In one attempt to develop a feed mix for cows, a restriction limiting the total amount of molasses was included to insure that the resultant feed could be processed by the manufacturing equipment which pressed the feed into pellets. It turns out that molasses is cheap and reasonably high in calcium and protein, and the cows love it. Thus, the optimal solution included as much molasses as possible, but the optimum feed was rejected by the manufacturer. Although he could manufacture it in pellet form, the molasses content would make the manure too soft to use as fertilizer.
If the children wish to eat only Krunchies, the housewife cannot lower the amount of Krunchies below 10 ounces, as a lower quantity would not contain at least 1 milligram of thiamine. Similarly, if the children wish to eat only Crispies, they must eat 20 ounces, for otherwise they would not get enough niacin. The only alternative solution left is a mixture of the two cereals—the housewife must determine if there exists a combination of the two which contains enough of the nutrients and is cheaper than the 10-ounce Krunchies solution.
An Illustrated Guide to Linear Programming by Dr. Saul I. Gass