Problem 6-06 (Algorithmic) 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 Clifton Springs Danville D2 $102 $90 D3 $96 $84 $120 $96 $114 $102 The plant capacities and customer orders are as follows Distributor Orders (units) D1 8000 D2 20000 D312000 D48000 Plant Capacity (units) Clifton Springs 20000 Danville 12000 How many units should each plant produce for each customer in order to maximize profits? Which customer demands will not be met? Choose correct network model and Show linear programming formulation. If the constant is "1" it must be entered in the box. If your answer is zero, enter "O" 102 Di D1 8000 96 102 C.S C.S 120 102 D2 20000 D2 102 D. 12000 12000 114 12000 D3 12000 D3 Dummy16000 16000 Dummy 114 12 D4 8000 D4 96 Di Di 102 102 C.S. 20000 .s 120 90 20000D2 D2 20000 12000D 12000 12000 D3 D3 12000 Dummy 16000 16000 Dummy 120 0 D4 D4 Let xo-amount of units produced by plant node i for customer node j. Max X11 x21 X22 X12 X24 X12+ X13+ X31+ X13+ X21 + X14+ X23 x32 X33+ x34 s.t. X11+ X23+ X22 x24 x31+ Dummy X32 X33 X34 S X11 x31 X21 X12 X22 X32 X13 X23 X33 X14 X24 X34 20 for all i, j Cost, $ Units Clifton Springs D1 Clifton Springs D2 Clifton Springs D3 Clifton Springs D4 Danville-D1 Danville D2 Danville D3 Danville D4 Dummy D1 Dummy- D2 Dummy- D3 ou Dummy D4 Total Cost demand has a shortfall of demand of is not satisfied Problem 6-06 (Algorithmic) 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 Clifton Springs Danville D2 $102 $90 D3 $96 $84 $120 $96 $114 $102 The plant capacities and customer orders are as follows Distributor Orders (units) D1 8000 D2 20000 D312000 D48000 Plant Capacity (units) Clifton Springs 20000 Danville 12000 How many units should each plant produce for each customer in order to maximize profits? Which customer demands will not be met? Choose correct network model and Show linear programming formulation. If the constant is "1" it must be entered in the box. If your answer is zero, enter "O" 102 Di D1 8000 96 102 C.S C.S 120 102 D2 20000 D2 102 D. 12000 12000 114 12000 D3 12000 D3 Dummy16000 16000 Dummy 114 12 D4 8000 D4 96 Di Di 102 102 C.S. 20000 .s 120 90 20000D2 D2 20000 12000D 12000 12000 D3 D3 12000 Dummy 16000 16000 Dummy 120 0 D4 D4 Let xo-amount of units produced by plant node i for customer node j. Max X11 x21 X22 X12 X24 X12+ X13+ X31+ X13+ X21 + X14+ X23 x32 X33+ x34 s.t. X11+ X23+ X22 x24 x31+ Dummy X32 X33 X34 S X11 x31 X21 X12 X22 X32 X13 X23 X33 X14 X24 X34 20 for all i, j Cost, $ Units Clifton Springs D1 Clifton Springs D2 Clifton Springs D3 Clifton Springs D4 Danville-D1 Danville D2 Danville D3 Danville D4 Dummy D1 Dummy- D2 Dummy- D3 ou Dummy D4 Total Cost demand has a shortfall of demand of is not satisfied