Qunatitative Methods

LINEAR PROGRAMMING Some examples The simplex method matrix verbalism Sensitivity analysis Duality theory  spokesperson 1: mesh maximization The firm Hikea produces four fibers of presss. Producing one cupboard requires some wintry processing time in twain departments (hours/unit). Question: How many a(prenominal) cupboards of each type should be produced by the firm if its documentary is to maximize its total do vertical?  model process Situation ? Modeling, entropy collection, ... ? Model ? Weaknesses ? instruction execution of decisions REAL WORLD ? recital ? ? declaration ? Conclusions of the model larboard MATHEMATICS Example 1: information collection A1 cabinetmaking 4 A2 9 A3 7 A4 1 Available hours 6 000 Packaging Profit/unit (euro/unit)??? 1 12 1 20 3 18 4 10 4 000 A mathematical model Decision variables: xi = human action of cupboards of type i produced, i = 1,2,3,4.

Objective function (to be maximized): profit = z = 12 x1 + 20 x2 + 18 x3 + 10 x4 A mathematical model Objective function (to be maximized): profit = z = 12 x1 + 20 x2 + 18 x3 + 10 x4 Constraints: 4 x1 + 9 x2 + 7 x3 + x4 ? 6000 x1 + x2 + 3 x3 + 4 x4 ? 4000 x1, x2, x3, x4 ? 0 Optimal solution (computed by Excel) x1 = 4000/3 = 1333,3 x2 = x3 = 0 x4 = 2000/3 = 666,7 z = 22666,7 These ranges foregather all the constraints and no different feasible values would fruit a higher value of the objective function z. Modeling process Situation ? Modeling, data collection, ... ? Model ? Weaknesses ? Implementation of decision s REAL WORLD ? Interpretation ? ? Solutio! n ? Conclusions of the model INTERFACE MATHEMATICS Optimal solution x1 = 4000/3 = 1333,3 x2 = x3 = 0 x4 = 2000/3 = 666,7 z = 22666,7 Is this an acceptable solution? Should we specify the model? Sensitivity analysis allow us trim back for instance: - at least vitamin D cupboards of type A1 and A4 - at least 100 cupboards of type A2 and A3. How does this fall upon the previous best solution?...If you want to get a full essay, exhibition it on our website: OrderCustomPaper.com

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