# 3 4 3 2 1 x x x x 15 80001 15 3 1 4 32 1 x xx x 15

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.03.04321XXXX15.080001.015.03.01.04321XXXX15.080003.02.02.02.04321XXXX0,,,4321XXXX
Dell - Internal Use - ConfidentialA Comment About ScalingNotice that the coefficient for X2in the ‘corn’ constraint is 0.05/8000 = 0.00000625.As Solver solves our problem, intermediate calculations must be done that make coefficients large or smaller.Storage problems may force the computer to use approximations of the actual numbers.Such ‘scaling’ problems sometimes prevents Solver from being able to solve the problem accurately.Most problems can be formulated in a way to minimize scaling errors...
Dell - Internal Use - ConfidentialRe-Defining the Objective FunctionMinimize the total cost of filling the order.MIN: 250X1+ 300X2+ 320X3+ 150X4
Dell - Internal Use - ConfidentialRe-Defining the ConstraintsProduce 8,000 pounds of feedX1+ X2+ X3+ X4= 8Mix consists of at least 20% corn Mix consists of at least 15% grainMix consists of at least 15% mineralsNonnegativity conditions2.081.02.005.03.04321XXXX15.081.015.03.01.04321XXXX15.083.02.02.02.04321XXXX0,,,4321XXXX
Dell - Internal Use - ConfidentialA Comment About ScalingEarlier the largest coefficient in the constraints was 8,000 and the smallest is 0.05/8 = 0.00000625.Now the largest coefficient in the constraints is 8 and the smallest is 0.05/8 = 0.00625.The problem is now more evenly scaled.
Dell - Internal Use - ConfidentialThe Use Automatic Scaling OptionThe Solver Parameters dialog box has an option labeled “Use Automatic Scaling”. This option button actually has no effectfor LP problems in Excel 5.0 & 7.0 (unless you install the upgraded Solver DLL mentioned in the preface), but it does work in Excel 8.0.
Dell - Internal Use - ConfidentialThe Assume Linear Model OptionThe Solver Parameters dialog box has an option labeled “Assume Linear Model”. When you select this option Solver performs some tests to verify that your model is in fact linear. These test are not 100% accurate & often fail as a result of a poorly scaled model.If Solver tells you a model isn’t linear when you know it is, try solving it again. If that doesn’t work, try re-scaling your model.
Dell - Internal Use - ConfidentialImplementing the ModelSee file Lesson2-5.xls
Dell - Internal Use - ConfidentialA Production Planning Problem:The Upton CorporationUpton is planning the production of their heavy-duty air compressors for the next 6 months.Beginning inventory = 2,750 units Safety stock = (at least)1,500 unitsUnit carrying cost = 1.5% of unit production costMaximum warehouse capacity = 6,000 units12 3456Unit Production Cost\$240\$250\$265\$285\$280\$260Units Demanded1,0004,5006,0005,5003,5004,000Maximum Production4,0003,5004,0004,5004,0003,500Minimum Production2,0001,7502,0002,2502,0001,750Month
Dell - Internal Use - Confidential