By Dr. Saul I. Gass
Unique, nontechnical creation covers easy ideas of linear programming and its courting to operations examine; geometric interpretation and challenge fixing, resolution strategies, community difficulties, even more. Appendix deals specific statements of definitions, theorems, and strategies, extra computational approaches. merely high-school algebra wanted. Bibliography.
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Additional info for An Illustrated Guide to Linear Programming
Although an important branch of applied mathematics in its own right, linear programming and its extensions are rightly subsumed within the more general field of scientific decision-making, that is operations research. In the past, OR gave the impression that its main preoccupation was the optimization of large, integrated systems like complex production-distribution facilities. In reality, however, the problems which could be resolved were subsystems of subsystems like a simplified transportation problem.
Finally, let d1, d2, d3, d4, d5, d6, d7, be the number of dirty napkins which are not sent to a laundry on the corresponding day. As we want to minimize the total cost of maintaining the proper inventory of clean napkins, it does not pay to buy more napkins than needed for the current day, or to send out a napkin to be laundered unless it will be used at a future time. For the first day of operation, i. , on Monday, we must buy exactly the number needed. As we expect five guests, we conclude that n1 = 5.
First, there is one equation too many, in that any one of them is implied by the remaining ones. For example, if we drop the first equation, it can be found by adding the last three and then subtracting the second. A more important point, however, is that if we solve the problem using the standard computational procedures of linear programming, we will determine an optimum solution whose values of the variables, the xij’s, are in terms of whole numbers. It was tacitly assumed that the xij’s must be in integers—we cannot ship 3¾ refrigerators!
An Illustrated Guide to Linear Programming by Dr. Saul I. Gass
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