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help-homework3 - Homework 3 Some help for difficult...

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Unformatted text preview: Homework 3 Some help for difficult problems The dual of non-standard forms If Xi≥0, then the dual has the "proper" ≥0, form for the ith restriction. form If that dual is a max, then the ith If restriction will be ≤. restriction If that dual is a min, then the ith If restriction will be ≥. The dual of non-standard forms If Xi≤0, then the dual has the "wrong" ≤0, form for the ith restriction. form If that dual is a max, then the ith If restriction will be ≥. restriction If that dual is a min, then the ith If restriction will be ≤. Duals of non-standard forms Duals If Xi is unrestricted, then constraint i in If the dual will be an equality. the McCarl and Spreen have a chart you can McCarl refer to when developing duals for nonrefer standard forms. standard Conversion to standard form An inequality going the "wrong way" is An multiplied through by -1 and "flipped" to the correct way. An equality becomes two constraints, An one a LE the other a GE. Then, the one that is the "wrong way" is multiplied through by -1 and "flipped" to the correct way. Conversion to standard form If Xi≤0, replace with Xineg and multiply ≤0, every coefficient in the column by -1. every If Xi unrestricted, use Xipos and Xineg. If Xipos will have same coffecients as Xi. Xineg will have the coefficients multiplied by -1. Multiple uses for products Multiple Each possible use for a product must Each have its very own column. have You can't share the column with other You products being converted to the same item or you will be counting the use multiple times. multiple Example I can produce corn or sugar cane and sell can the raw product. Or I can use the corn or sugar cane to Or produce a syrup. Sample solutions follow. Syrup problem production constraint transfer yield corn transfer yield sugar can syrup transfer -corn syrup transfer - cane total syrup syrup limit answers Produce Corn (acres) -$90.00 1 -95 Produce Cane (acres) -$80.00 1 Sell Corn (bu) $3.00 Sell Cane (tons) $30.00 Corn for Cane for make make total Syrup Syrup syrup corn syrup cane syrup (bu) (tons) (gallons) (gallons) (gallons) $10.00 1 -35 1 1 1 -3 1 -8 1 10.53 189.47 0.00 6631.58 1000.00 Note the large number of activities. 0.00 1 1 3000.00 0.00 -1 1 3000.00 RHS LE LE LE LE LE EQ LE 200 0 0 0 0 0 3000 212842.11 200.00 0.00 0.00 0.00 0.00 0.00 3000.00 meat problem You need separate variables for grinding You different cuts into hamburger (3 variables). variables). If you don't use separate variables, the If model over-counts the amount of product needed to make hamburger. Incorrect Specification Meat Variety Hamb Chuck Round Steak Loin Rib Misc 0.6 0.85 0.5 0.75 1.2 0.8 1.2 0.2 chuckt -0.29 1 1 roundt -0.22 1 1 steakt -0.19 1 loint -0.16 1 1 ribt -0.09 1 misct -0.05 1 hlimit 1 meatlim 1 var trans 1 answers 569 27 0 165 125.2 108.1 91.04 51.21 28.45 rc 0 0 0 0 0 0 0 0 0 le 0 le 0 le 0 le 0 le 0 le 0 le 50 le 569 le 27 limits SP 462.3 0.0 0.5 0.0 0.8 0.0 1.2 0.0 0.8 0.0 1.2 0.0 0.2 0.0 0.3 569.0 0.8 27.0 0.6 Juice Problem How many activities do you need? Production – 3 activities (3 varieties) Sales of fruit – 2 activities (2 varieties can be Sales sold as fruit) sold Putting aside fruit for juice (3 activities, one for Putting each variety of fruit) each Using the set-aside fruit for a kind of juice (6 Using activities, 2 types of juice times 3 sets of activities for putting fruit aside for juice) activities Selling juice (2 activities) Selling Juice Problem – part a Juice Restrictions (rows) amount of land to produce oranges market limit for fresh Rich Fibers 3 transfer rows to take produced fruit and distribute to transfer fresh market or the set-aside for juice fresh 3 transfer rows to move set-aside fruit to juice A and/or transfer Juice B production. Juice Two "blending" restrictions for A and B (volume) Two quality restrictions for juice A Two quality restrictions for juice B. Two final obj value = $118,028.99 ...
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