Problem 6-06 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 many units 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 costs between 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: Customer D D2 D D4 Plant Clifton Springs $32 $34 $32 $28 $40 $38 Danville $34 $30 The plant capacities and customer orders are as follows: Plant Capacity (units) Distributor Orders (units) Di 2000 D2 5000 Clifton Springs 5000 Danville 3000 Dy 3000 DA 2000 How many units should each plant produce for each customer in order to maximize profits? Which customer demands will not be met? Show your network model and linear programming WOWODU W UZI Calciator 12 DI 2000 2000 DI 12 14 5000 CS cs 5000 32 40 14 SOCO 49 D2 D2 0 5000 0 O 3000 D 0 D 3000 32 28 D 3000 3000 D3 0 544 40 4000 28 Dum 40 Dum 4000 38 38 0 D4 2000 2000 14 34 DI 2000 2000 DI 32 12 0 34 5000 C.S. 5000 32 40 5000 02 5000 D2 14 40 3000 D 28 3000 28 38 32 D3 3000 3000 0 4000 0 38 40 0 D4 2000 2000 D4 Lety amount of units produced by plant nade i for customer nodej. IMA + 2x x13+ X14+ 21+ EZX X24 + TEX X321+ -EX PEX Ist x+ X12 + x3+ DIX X21+ *221+ . TEX x321+ X331+ SEX X11 X21 TEX X12 22 X23 133 X24 VOX Xy 20 for all, Xy 20 for all/, Units Cost $ Clifton Springs - Di Clifton Springs - D2 Clifton Springs - 3 Clifton Springs - D4 Danville - Di Danville - D2 Danville - D3 Danville - D4 Dummy - Di Dummy-D2 Dummy - D3 Dummy - D4 Total Cost $ Customer 2 demand has a shortfall of 1000 Customer 3 demand of 3000 is not satisfied Problem 6-06 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 many units 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 costs between 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: Customer Plant D D2 D D4 Clifton Springs $32 $34 $32 $40 Danville $34 $30 $28 $38 The plant capacities and customer orders are as follows: Plant Capacity (units) Distributor Orders (units) Clifton Springs SOOD D: 2000 D25000 Danville 300D D3 3000 D4 2000 How many units should each plant produce for each customer in order to maximize profits? Which customer demands will not be met? Show your network model and linear programming formulation Note: Dummy origin has supply of 4000. 00) (W) 12 DI DI 2000 2000 0 34 CS CS 5000 5000 32 40 5000 D2 D2 5000 0 3000 D 3000 D. 10 12 28 3000 D3 D) 3000 o 32 DI 2000 2000 D 34 32 34 5000 C.S. CS. 5000 32 34 40 40 D2 5000 5000 0 D2 0 0 3000 D 0 D 3000 32 0 28 D3 3000 3000 D3 0 34 40 4000 Dum 28 40 Dum 4000 38 0 D4 2000 2000 D4 14 DI 2000 2000 DI 12 32 34 5000 CS 32 CS 5000 40 42 34 D2 34 5000 5000 D2 40 0 3000 D 128 D 3000 38 28 32 D3 3000 3000 D3 0 4000 0 Dum 38 Dum 4000 40 D4 2000 2000 D4 Let xy amount of units produced by plant node i for customer nodej. Mas + x X12 - ILEX 14 x21 X22 EZX + *241. + TEX x32 X331+ 34 Is.t. *121+ CTX *14 21+ 22+ EX PEX +TE X321+ + SEX SIMEX IEX X21 X31 ZEX X22 X32 ETX EZK I+ EEX 24 X Xg 20 for all Let x - amount of units produced by plant node i for customer nodej, Max *13+ X14+ + FOX 21+ 23 X24 + +IX LEX PEX S. x11+ X121+ + ELX X21+ x22+ x231+ X31+ X321+ + EEX SEX LEX . TEX CEX 22 + X23 CEX X14 X24 + x- Xy 20 for all / Units Cost Clifton Springs - Di Clifton Springs - D2 Clifton Springs - 3 Clifton Springs - D4 Danville-D1 Danville-D2 Units Cost Clifton Springs - Di Clifton Springs - D2 Clifton Springs - D3 Clifton Springs - D4 Danville - D1 Danville - D2 Danville - D3 Danville - D4 Dummy - D1 Dummy - D2 Dummy - D3 Dummy - D4 Total Cost $ Customer 2 demand has a shortfall of 1000 V Customer 3 y demand of 3000 is not satisfied. Problem 6-06 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 many units 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 costs between 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: Customer D D2 D D4 Plant Clifton Springs $32 $34 $32 $28 $40 $38 Danville $34 $30 The plant capacities and customer orders are as follows: Plant Capacity (units) Distributor Orders (units) Di 2000 D2 5000 Clifton Springs 5000 Danville 3000 Dy 3000 DA 2000 How many units should each plant produce for each customer in order to maximize profits? Which customer demands will not be met? Show your network model and linear programming WOWODU W UZI Calciator 12 DI 2000 2000 DI 12 14 5000 CS cs 5000 32 40 14 SOCO 49 D2 D2 0 5000 0 O 3000 D 0 D 3000 32 28 D 3000 3000 D3 0 544 40 4000 28 Dum 40 Dum 4000 38 38 0 D4 2000 2000 14 34 DI 2000 2000 DI 32 12 0 34 5000 C.S. 5000 32 40 5000 02 5000 D2 14 40 3000 D 28 3000 28 38 32 D3 3000 3000 0 4000 0 38 40 0 D4 2000 2000 D4 Lety amount of units produced by plant nade i for customer nodej. IMA + 2x x13+ X14+ 21+ EZX X24 + TEX X321+ -EX PEX Ist x+ X12 + x3+ DIX X21+ *221+ . TEX x321+ X331+ SEX X11 X21 TEX X12 22 X23 133 X24 VOX Xy 20 for all, Xy 20 for all/, Units Cost $ Clifton Springs - Di Clifton Springs - D2 Clifton Springs - 3 Clifton Springs - D4 Danville - Di Danville - D2 Danville - D3 Danville - D4 Dummy - Di Dummy-D2 Dummy - D3 Dummy - D4 Total Cost $ Customer 2 demand has a shortfall of 1000 Customer 3 demand of 3000 is not satisfied Problem 6-06 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 many units 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 costs between 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: Customer Plant D D2 D D4 Clifton Springs $32 $34 $32 $40 Danville $34 $30 $28 $38 The plant capacities and customer orders are as follows: Plant Capacity (units) Distributor Orders (units) Clifton Springs SOOD D: 2000 D25000 Danville 300D D3 3000 D4 2000 How many units should each plant produce for each customer in order to maximize profits? Which customer demands will not be met? Show your network model and linear programming formulation Note: Dummy origin has supply of 4000. 00) (W) 12 DI DI 2000 2000 0 34 CS CS 5000 5000 32 40 5000 D2 D2 5000 0 3000 D 3000 D. 10 12 28 3000 D3 D) 3000 o 32 DI 2000 2000 D 34 32 34 5000 C.S. CS. 5000 32 34 40 40 D2 5000 5000 0 D2 0 0 3000 D 0 D 3000 32 0 28 D3 3000 3000 D3 0 34 40 4000 Dum 28 40 Dum 4000 38 0 D4 2000 2000 D4 14 DI 2000 2000 DI 12 32 34 5000 CS 32 CS 5000 40 42 34 D2 34 5000 5000 D2 40 0 3000 D 128 D 3000 38 28 32 D3 3000 3000 D3 0 4000 0 Dum 38 Dum 4000 40 D4 2000 2000 D4 Let xy amount of units produced by plant node i for customer nodej. Mas + x X12 - ILEX 14 x21 X22 EZX + *241. + TEX x32 X331+ 34 Is.t. *121+ CTX *14 21+ 22+ EX PEX +TE X321+ + SEX SIMEX IEX X21 X31 ZEX X22 X32 ETX EZK I+ EEX 24 X Xg 20 for all Let x - amount of units produced by plant node i for customer nodej, Max *13+ X14+ + FOX 21+ 23 X24 + +IX LEX PEX S. x11+ X121+ + ELX X21+ x22+ x231+ X31+ X321+ + EEX SEX LEX . TEX CEX 22 + X23 CEX X14 X24 + x- Xy 20 for all / Units Cost Clifton Springs - Di Clifton Springs - D2 Clifton Springs - 3 Clifton Springs - D4 Danville-D1 Danville-D2 Units Cost Clifton Springs - Di Clifton Springs - D2 Clifton Springs - D3 Clifton Springs - D4 Danville - D1 Danville - D2 Danville - D3 Danville - D4 Dummy - D1 Dummy - D2 Dummy - D3 Dummy - D4 Total Cost $ Customer 2 demand has a shortfall of 1000 V Customer 3 y demand of 3000 is not satisfied