By H. Kaiser, Kent D. Messer
Mathematical Programming types for Agriculture, Environmental, and source Economics offers a entire review of mathematical programming versions and their purposes to actual international and critical difficulties confronting agricultural, environmental, and source economists. not like such a lot mathematical programming books, the relevant concentration of this article is on functions of those strategies and types to the fields of agricultural, environmental, and source economics. the 3 basic pursuits of the e-book are to supply the reader with: (1) a degree of history enough to use mathematical programming recommendations to actual global coverage and enterprise to behavior stable learn and research, (2) numerous functions of mathematical programming to big difficulties within the parts of agricultural, environmental, and source economics, and (3) an organization beginning for instruction to extra complicated, Ph.D. point books on linear and/or nonlinear programming. regardless of its introductory nature, the textual content locations major emphasis on genuine global functions of mathematical programming to selection problems. a wide range of examples and case experiences are used to exhibit a few of the programming strategies on hand to choice analysts.
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Additional resources for Mathematical Programming for Agricultural, Environmental, and Resource Economics
To represent the amount of unused resource 1, define slack variable 1 (s1), which equals: s1 ϭ 600 Ϫ x Ϫ y. Rearranging this equation to put the constant on the RHS yields: x ϩ y ϩ s1 ϭ 600. To include a slack variable for a Յ type constraint add it to the constraint and replace the Յ restriction with an equality restriction. qxd 12/1/10 2:00 PM Page 32 32 PART 1 LINEAR PROGRAMMING Since slack variables do not contribute to the objective function value, they are included as activities in the objective function with zero objective function coefficients.
The solution to this problem is: x* ϭ 100 Ϫ y*, y* ϭ 100 Ϫ x*, Z* ϭ 100. The existence of multiple optimal solutions is not a problem. In fact, such a situation is beneficial, as it gives the decision maker more flexibility in pursuing the optimal solution. That is, it offers the decision maker alternatives, which should be preferred. In such cases, alternative decision rules may be used by the decision maker in selecting one of the optimal solutions. For example, a decision maker may wish to choose an option that specializes in either x or y if the level of profitability is the same among a set of different optimal solutions.
Since most of the concepts are analogous to the previous section, this section will emphasize the steps involved in the solution procedures. If any of the concepts are unclear, consult the previous section for more detail. Consider the following LP problem written in general form. qxd 12/1/10 2:00 PM CHAPTER 1 Page 27 INTRODUCTORY CONCEPTS AND THE GRAPHICAL APPROACH TO LINEAR PROGRAMMING 27 The optimal solution to minimization problems is found exactly as were found in the maximization problem using the following steps.