By Dr. Saul I. Gass
Enjoyable, nontechnical creation covers uncomplicated suggestions of linear programming and its courting to operations examine; geometric interpretation and challenge fixing, resolution recommendations, community difficulties, even more. Appendix bargains exact statements of definitions, theorems, and strategies, extra computational techniques. simply high-school algebra wanted. Bibliography.
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Additional resources for An Illustrated Guide to Linear Programming
There are standard applications of programming techniques found in the areas of agriculture, petrochemicals, paper manufacturing, transportation, production scheduling and inventory control, military and defense, engineering, economics, to cite just a few. A bibliography of applications is given in the Appendix. We shall deal with a few such applications in order to develop the fundamentals of linear programming. , operations research or management science. OPERATIONS RESEARCH AND MODELS When we mean to build, We first survey the plot, then draw the model; And when we see the figure of the house, Then must we rate the cost of the erection.
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. This rather earthy example illustrates how an analyst must go about developing a mathematical model which produces solutions that can be put to work. It is an evolutionary process and calls for the close interactions of the people with the problem and the man with the model.
A solution to the problem must have Similarly, for niacin, we must have and for calories, The amount of each food eaten must be zero or a positive amount; i. , K ≥ 0 and C ≥ 0. Finally, the total cost of the breakfast menu is given by Putting the above together, the housewife’s breakfast-menu problem is to find values of K and C which minimizes the total cost subject to The reader can readily check that our two previous menus K = 10, C = 0 and K = 0, C = 20 satisfy the above inequalities. The minimum solution is when K = 4 ounces and C = 2 ounces, with a total cost of 26 cents.
An Illustrated Guide to Linear Programming by Dr. Saul I. Gass