Linear Programming Essay -- Computer Science

running(a) Programming Part Apresentation analog 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 that go off be used to chain reactor with the difficulty of allocating limited facilitiesand resources among many alternative uses in auberge to occur out the best benefits. The main objective of the elongated programming problemin management is to maximize profit or minimize cost. Linearprogramming has a wide variety of applications. It is used by crudecompanies to determine the best mixture of ingredients for blendinggasoline. It is also plays an important purpose 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, depute personnel in human resources management.Applic ationsOne of the most important applications of linear programming is theformulation of blends. Blending problems appear whenever a manager must(prenominal) decide how to blend tow or more recourse in exhibition to produce oneor more products. In these situations, the recourses a good deal containsone or more essential components that must be composite in a given patternand the final product pass on contains specific percentage of theessential components. In most of these applications management and sohas to decide how much of all(prenominal) recourse to purchase in order tosatisfy product specification and produce demand at minimal cost.Blending problems occur frequently in the petroleum industry( much(prenominal) asblending crude oil to produce different octane gasoline), chemicalindustry( such as blending chemicals to produce fertilizers, weekkillers, and so on), and food industry( such as blending inputingredients to product soft drinks, soups, and so on).Linear program ming is also a very 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 order to meetthe product demand requirements, given limitations on labor capacity, mechanism hours capacity and so on, at the same time, to pull out the costof production to minimum. The... ...simultaneously, we get X=2/3, Y=7, mess them into objective function40X+20Y we get a profit of 166.67. The difference mingled with this profitand the original max-profit is 166.67-160=6.67, which means the dual toll for increasing/decrease in purchasing 1 pig, is 6.67.Economic meaning for shadow scatheThe economics meaning of shadow price is the improvement in theoptimal value of the objective function per unit increase in the right side of the constraint. In a profit maximization problem,the dual price is the same as the shadow price. Managers could getinfo rmation from the performance of each constraint and therefore make finales 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 weigh of bushels rather than increasethe amount of pigs.ReferenceThe 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. . sixth Edition, West, Chapter 4.