Please help with constraints. Question provided below with data. Not sure why the dummy constraint is incorrect. (ii) linear programming formulationLet Xj= number of units i shipped to client j, using the indices from the given table. (It may be necessary to combine plants or distributors in a single node in order to solve this problem. Use index number 5 for this type of node. Enter "DNE" in any unusedanswer blanks.)32x11+34x12+ 32x13+ 40x14+ 34x21 + 30x22 + 28x23+ 38x24Маxs.t.+x,+Orders from Clifton Springs X11 †*12 + *13 x14< 5000+++3000Orders from Danville X21 X22 † *23 † 24Orders from/for Dummy Node X31 † X32 † X33 + X34 < 4000Orders for D, X11+x21 < 2000Orders for D, X12+x22< 5000Orders for D3 X13 +x23 < 3000Orders for D4 *14+ x24 < 2000Xj 2 0 for all i, j. Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of Klein's customers have already placed orders that together exceed the combined capacity of Klein's two plants. Klein's management faces the problem of deciding how manyunits it should supply to each customer. Because the four customers are in different industries, different prices can be charged because of the various industry pricing structures. However, slightly different production costs at the two plants and varying transportation costsbetween the plants and customers make a "sell to the highest bidder" strategy unacceptable. After considering price, production costs, and transportation costs, Klein established the following profit per unit for each plant-customer alternative.CustomerPlant31D21D3D4Clifton Springs$32$34$32$40Danville$34$30$28$38The plant capacities and customer orders are as follows.PlantCapacity (units)Distributor Orders (units)Clifton Springs5,000D12,000Danville3,000D25,000D33,000D42,000

(H) linear programming formulation Let x- number of units i shipped to client j, using the indices from the given table. (It may be necessary to combine plants or distributors in a single node in order to solve this problem. Use index number 5 for this type of node. Enter "DNE" in any unused answer blanks.) Max 32r1 +34x,2 + 32r13 + 40x14 + 34x21 + 30x + 28x + 38x24 s.t. Orders from Clifton Springs X11 +x12 +x13+x14 < 5000 Orders from Danville X21 +X22 +x23 + X24S3000 Orders from/for Dummy Node X3I +x32 + x33 +x34S 4000 Orders for D, Xu +x21 S 2000 Orders for D, X12 +X22S 5000 Orders for D, X13 + X23 < 3000 Orders for D. X14 +x24S 2000 Xy 2 0 for all 1, j.

(H) linear programming formulation Let x- number of units i shipped to client j, using the indices from the given table. (It may be necessary to combine plants or distributors in a single node in order to solve this problem. Use index number 5 for this type of node. Enter "DNE" in any unused answer blanks.) Max 32r1 +34x,2 + 32r13 + 40x14 + 34x21 + 30x + 28x + 38x24 s.t. Orders from Clifton Springs X11 +x12 +x13+x14 < 5000 Orders from Danville X21 +X22 +x23 + X24S3000 Orders from/for Dummy Node X3I +x32 + x33 +x34S 4000 Orders for D, Xu +x21 S 2000 Orders for D, X12 +X22S 5000 Orders for D, X13 + X23 < 3000 Orders for D. X14 +x24S 2000 Xy 2 0 for all 1, j.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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