Linear Programming Essay -- Computer Science

Linear program Part AIntroductionLinear programming was developed by George B. Dantzig in 1947 as atechnique for planning the diversified activities of the U.S agate lineForce. Linear programming is a powerful mathematical technique that fag end be used to deal with the problem of allocating limited facilitiesand resources among many alternative uses in order to find out theoptimal benefits. The main mark of the linear programming problemin management is to maximize bring in or minimize cost. Linearprogramming has a wide build of applications. It is used by oilcompanies to determine the best mixture of ingredients for blendinggasoline. It is also plays an important part in making the optimalschedules for transportation, production, and construction. Inaddition, linear programming is a flexible problem-solving tool forportfolio selection in finance, bud createing advertising expenditures inmarketing, assigning personnel in human resources management.Applications atomic number 53 of the most important applications of linear programming is theformulation of blends. Blending problems expect whenever a managermust decide how to blend tow or more(prenominal) recourse in order to garden truck oneor more products. In these situations, the recourses often containsone or more indispensable components that must be mixed in a assumption moldand the final product will contains specific percentage of theessential components. In most of these applications management thenhas to decide how much of each recourse to purchase in order tosatisfy product specification and gravel demand at minimum cost.Blending problems occur frequently in the petroleum industry( such asblending crude oil to produce different octane gasoline), chemicalindustry( such as blending chemicals to produce fertilizers, workweekkillers, and so on), and food industry( such as blending inputingredients to product soft drinks, soups, and so on).Linear programming is also a rattling useful tool that can be used to dealwith problems in manufacturing industry, such as the product-mixproblem. In this situation, the objective of the manager is todetermine the production levels that will allow the company to meetthe product demand requirements, given limitations on labor capacity,machine hours capacity and so on, at the same time, to make the costof production to minimum. The... ...simultaneously, we get X=2/3, Y=7, plug them into objective function40X+20Y we get a meshing of 166.67. The difference between this profitand the original max-profit is 166.67-160=6.67, which means the threefold determine for increasing/decreasing in purchasing 1 pig, is 6.67.stinting meaning for shadow priceThe economics meaning of shadow price is the improvement in theoptimal value of the objective function per building block increase in theright-hand side of the constraint. In a profit maximization problem,the dual price is the same as the shadow price. Managers could getinformation from the pe rformance of each constraint and therefore make terminations on any changes in a particular input factor or resource inorder to increase profit. In this case, to get more profit, the farmeris recommended to increase the number of bushels rather than increasethe amount of pigs. fibreThe Quantitative methods for business decision with cases, LawrenceL. Lapim, 6th Edition, Dryden, Chapter 9.An introduction to management science-quantitative approaches todecision making, David R.Anderson, Dennis J. Sweeney, Thomas A.Williams. . 6Th Edition, West, Chapter 4.