Linear Programming Essay -- Computer Science

Linear Programming Part AIntroductionLinear programming was developed by George B. Dantzig in 1947 as atechnique for planning the diversified activities of the U.S AirForce. Linear programming is a powerful mathematical technique thatcan be used to deal with the occupation of allocating limited facilitiesand resources among many alternative uses in order to find out theoptimal benefits. The main objective of the linear programming problemin solicitude is to maximize profit or minimize cost. Linearprogramming has a wide variety of applications. It is used by oilcompanies to determine the best garland 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, budgeting advertising expenditures inmarketing, assigning personnel in human resources management.ApplicationsOne of the most important applications of linear programming is theformulation of blends. Blending problems appear whenever a managermust decide how to blend tow or more recourse in order to produce oneor more products. In these situations, the recourses often containsone or more essential components that must be mixed in a given patternand the final product ordain contains specific percentage of theessential components. In most of these applications management thenhas to decide how much of each recourse to purchase in order to replete product specification and produce demand at minimum cost.Blending problems occur frequently in the petroleum industry( such asblending everlasting(a) oil to produce different octane gasoline), chemicalindustry( such as blending chemicals to produce fertilizers, weekkillers, and so on), and food industry( such as blending remarkingredients to product soft drinks, soups, and so on).Linear programming is also a very useful tool that can be used to dealwith problems in manufac turing 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 profit of 166.67. The difference between this profitand the original max-profit is 166.67-160=6.67, which means the dualprice for increasing/ change magnitude in purchasing 1 pig, is 6.67.Economic meaning for shadow priceThe economics meaning of shadow price is the improvement in theoptimal rank of the objective function per unit 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 performance of each constraint and therefore makedecisions on any changes in a particular input grammatical constituent 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. mentionThe 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.