Problem 5-06 (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 customer 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 Di D DA D2 $136 $123 $160 $128 Clifton Springs Danville $136 $120 $112 $152 The plant capacities and customer orders are as follows: Plant Capacity (units) Distributor Orders (units) Clifton Springs 5000 Di 2000 D25000 Danville 3000 D33000 D&2000 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, entero. Note: Dummy origin has supply of 4000 ID () 136 2000 DI 2000 DI 128 128 0 1136 5000 5000 CS CS . 128 160 120 136 5000 D2 D2 5000 136 0 120 3000 D. 3000 112 102 152 128 3000 3000 D3 0 10 4000 Dummy 10 150 Dummy 4000 1 0 10 10 DA 2000 2000 DM CHD (iv) 128 2000 DI Di 2000 136 0 128 136 CS 5000 5000 CS 136 128 160 120 5000 D2 5000 0 0 3000 3000 D 0 125 112 0 3000 D3 0 D3 3000 116 129 160 Dummy 4000 4000 Dummy UE 152 152 0 2000 D4 D4 2000 x 20 for all 1, Ex DEX EX 1 SEX CZx CTX + + CEX + ITX TEX TEX + + 2x + COX SIPEX + TOX + CEX EX X21+ 221+ S ZEX + CEX + TTX X14 + 2x + CEX + TEX X24+ X34 + CIX x21 + + + ZTX + TEX Max X14+ X22+ COX Let xy = amount of units produced by plant node i for customer node). X13 X14 Xij 20 fo Units Cost, $ Clifton Springs - Di Clifton Springs - D2 Clifton Springs - D3 Clifton Springs - D4 Danville - Di Danville - D2 Danville - D3 Danville - D4 Dummy - Di Dummy - D2 Dummy - D3 Dummy - D4 Total Cost demand has a shortfall of demand of is not satisfied. Check My Work 3 more Check My Work uses remaining. Problem 5-06 (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 customer 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 Di D DA D2 $136 $123 $160 $128 Clifton Springs Danville $136 $120 $112 $152 The plant capacities and customer orders are as follows: Plant Capacity (units) Distributor Orders (units) Clifton Springs 5000 Di 2000 D25000 Danville 3000 D33000 D&2000 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, entero. Note: Dummy origin has supply of 4000 ID () 136 2000 DI 2000 DI 128 128 0 1136 5000 5000 CS CS . 128 160 120 136 5000 D2 D2 5000 136 0 120 3000 D. 3000 112 102 152 128 3000 3000 D3 0 10 4000 Dummy 10 150 Dummy 4000 1 0 10 10 DA 2000 2000 DM CHD (iv) 128 2000 DI Di 2000 136 0 128 136 CS 5000 5000 CS 136 128 160 120 5000 D2 5000 0 0 3000 3000 D 0 125 112 0 3000 D3 0 D3 3000 116 129 160 Dummy 4000 4000 Dummy UE 152 152 0 2000 D4 D4 2000 x 20 for all 1, Ex DEX EX 1 SEX CZx CTX + + CEX + ITX TEX TEX + + 2x + COX SIPEX + TOX + CEX EX X21+ 221+ S ZEX + CEX + TTX X14 + 2x + CEX + TEX X24+ X34 + CIX x21 + + + ZTX + TEX Max X14+ X22+ COX Let xy = amount of units produced by plant node i for customer node). X13 X14 Xij 20 fo Units Cost, $ Clifton Springs - Di Clifton Springs - D2 Clifton Springs - D3 Clifton Springs - D4 Danville - Di Danville - D2 Danville - D3 Danville - D4 Dummy - Di Dummy - D2 Dummy - D3 Dummy - D4 Total Cost demand has a shortfall of demand of is not satisfied. Check My Work 3 more Check My Work uses remaining