By H. Kaiser, Kent D. Messer
Mathematical Programming versions for Agriculture, Environmental, and source Economics offers a accomplished evaluation of mathematical programming versions and their purposes to actual global and significant difficulties confronting agricultural, environmental, and source economists. in contrast to so much mathematical programming books, the crucial concentration of this article is on purposes of those concepts and types to the fields of agricultural, environmental, and source economics. the 3 basic pursuits of the publication are to supply the reader with: (1) a degree of historical past enough to use mathematical programming ideas to actual global coverage and company to behavior stable examine and research, (2) various functions of mathematical programming to special difficulties within the parts of agricultural, environmental, and source economics, and (3) a company origin for training to extra complex, Ph.D. point books on linear and/or nonlinear programming. regardless of its introductory nature, the textual content locations major emphasis on actual international purposes of mathematical programming to selection problems. a big selection of examples and case reports are used to show some of the programming strategies to be had to choice analysts.
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Extra resources for Mathematical Programming for Agricultural, Environmental, and Resource Economics
Sample text
The only difference between the LP representation of the PPF and the neoclassical economic representation of the PPF is that the LP PPF does not result in a smooth and continuous frontier, whereas the neoclassical PPF is smooth and continuous. qxd 12/1/10 2:00 PM CHAPTER 1 Page 21 INTRODUCTORY CONCEPTS AND THE GRAPHICAL APPROACH TO LINEAR PROGRAMMING 21 In this example, it is assumed that the firm is a “price taker”: that is, the firm cannot influence the price it receives for x or y by varying production.
5 units. 33) which is exactly equal to the RHS value, and hence the third structural constraint is binding. The optimal (minimum) value of the objective function is: Z* ϭ 500x* ϩ 750y*, or Z* ϭ 500(50) ϩ 750(25) ϭ $43,750. qxd 12/1/10 2:00 PM CHAPTER 1 Page 31 INTRODUCTORY CONCEPTS AND THE GRAPHICAL APPROACH TO LINEAR PROGRAMMING 31 determined. In this case, Constraints 1 and 3 are binding. 38) In this case, the simultaneous equation method has verified that the graphical solution is indeed correct.
Step 2: Draw an iso-cost line. An iso-cost line is a set of solutions lying on a line whose objective function values are all the same. Similar to iso-contribution lines, all iso-cost lines are parallel to one another since their slopes are the same. Also, assuming that the objective function coefficients are positive, the value of iso-cost lines decreases as they move towards the origin. Step 3: Continue to move the iso-cost line towards the origin until a further movement makes all points lying on the iso-cost line infeasible.