2. Introduction to Optimization and Linear Programming.pdf...

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Spreadsheet Modeling & Decision AnalysisA Practical Introduction to Management Science 5theditionCliff T. Ragsdale
Introduction to Optimization and Linear ProgrammingChapter 2
IntroductionWe all face decision about how to use limited resources such as:Oil in the earthLand for dumpsTimeMoneyWorkers
Mathematical Programming...MP is a field of operations research that finds the optimal, or most efficient, way of using limited resources to achieve the objectives of an individual of a business.a.k.a.Optimization
Applications of OptimizationDetermining Product MixManufacturingRouting and LogisticsFinancial Planning
Characteristics of Optimization ProblemsDecisionsConstraintsObjectives
General Form of an Optimization ProblemMAX (or MIN): f0(X1, X2, …, Xn)Subject to:f1(X1, X2, …, Xn)<=b1:fk(X1, X2, …, Xn)>=bk:fm(X1, X2, …, Xn)=bmNote: If all the functions in an optimization are linear, the problem is a Linear Programming (LP) problem
Linear Programming (LP) ProblemsMAX (or MIN):c1X1+ c2X2+ … + cnXnSubject to:a11X1+ a12X2+ … + a1nXn<= b1:ak1X1+ ak2X2+ … + aknXn>=bk:am1X1+ am2X2+ … + amnXn= bm
An Example LP ProblemBlue Ridge Hot Tubs produces two types of hot tubs: Aqua-Spas & Hydro-Luxes.There are 200 pumps, 1566 hours of labor, and 2880 feet of tubing available.Aqua-SpaHydro-LuxPumps11Labor 9 hours6 hoursTubing12 feet16 feetUnit Profit$350$300
5 Steps In Formulating LP Models:1. Understand the problem.2. Identify the decision variables.X1=number of Aqua-Spas to produceX2=number of Hydro-Luxes to produce3. State the objective function as a linear combination of the decision variables.

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