By Dr. Saul I. Gass
Unique, nontechnical advent covers simple ideas of linear programming and its courting to operations examine; geometric interpretation and challenge fixing, answer thoughts, community difficulties, even more. Appendix deals designated statements of definitions, theorems, and methods, extra computational systems. simply high-school algebra wanted. Bibliography.
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Additional info for An Illustrated Guide to Linear Programming
Our basic resource is time, and the selected program must be best in terms of how each individual interprets his expenditure of early morning time. From a personal point of view, ignoring the “bare” essentials, my program of action involves the putting on of six items of clothes: shoes, socks, trousers, shirt, tie, and jacket. A program of action is any order in which the clothes can be put on. There are 6 × 5 × 4 × 3 × 2 × l = 720 different orderings. Many of these are not feasible programs as they do not meet the constraints of society (socks over shoes) or are impractical (tie on before shirt).
Also, the total amount received by S1 from both factories is 10 + 0 = 10; S2 receives 1 + 7 = 8; and S3 receives 0 + 7 = 7. It is similar for the second solution. Assuming linearity of the cost of transportation, the total cost of the first solution is given by the expression and the cost of the second solution is For the solutions exhibited, the first has a lower cost, but the question remains as to whether there is another feasible solution which is cheaper. A shipping clerk who does not use linearprogramming techniques to aid him in solving the problem must rely heavily on his experience and intuition.
All the foregoing information, together with approximate air distances, are given in the following table: Here the objective is to minimize the total ton-miles. The optimum solution in terms of this objective has been computed and is given on page 21. The reader will find it instructive if he attempts to find the most efficient routing. A first attempt at a solution might go like this: Try to fill each requirement from the nearest source. Let McConnell get its 5 items and Davis-Monthan 3 of its 5 items from Oklahoma City.
An Illustrated Guide to Linear Programming by Dr. Saul I. Gass