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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 D4 $120 $114 $96 $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" Note: Dummy origin has supply of 16000 - amount of units produced by plant node i for customer node j. 68 X x21 56 X x23 64 X X11 68 X X12+ 64 X X13 60 X X22+ 76 X X24+ 0 0 X32 X34 20,000 1x21+ 12,000 1x31+ 1|VX34 8,000 1 x21 8,000 20,000 = 12,000 1|VX341=11 8,000 1 x22 1 x23 xi 2 0 for all i, j Units Cost, Clifton Springs D Clifton Springs D2 Clifton Springs D3 Clifton Springs D4 Danvlle D1 Danville -D2 Danville- D3 Danville D4 Dummy - D1 Dummy D2 Dummy D3 Dummy Da Total Cost 0 8,000 X544,000X 0 0 2,000 X 160,000 X 4,000 X 272,000X 0 0 2,000 X 152,000X 0 2,000 X 6,000 X 0 0 0 1,128,00 X Customer 2demand has a shortfall of 4000 Customer 3 demand of 4000 X is not satisfied 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 D4 $120 $114 $96 $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" Note: Dummy origin has supply of 16000 - amount of units produced by plant node i for customer node j. 68 X x21 56 X x23 64 X X11 68 X X12+ 64 X X13 60 X X22+ 76 X X24+ 0 0 X32 X34 20,000 1x21+ 12,000 1x31+ 1|VX34 8,000 1 x21 8,000 20,000 = 12,000 1|VX341=11 8,000 1 x22 1 x23 xi 2 0 for all i, j Units Cost, Clifton Springs D Clifton Springs D2 Clifton Springs D3 Clifton Springs D4 Danvlle D1 Danville -D2 Danville- D3 Danville D4 Dummy - D1 Dummy D2 Dummy D3 Dummy Da Total Cost 0 8,000 X544,000X 0 0 2,000 X 160,000 X 4,000 X 272,000X 0 0 2,000 X 152,000X 0 2,000 X 6,000 X 0 0 0 1,128,00 X Customer 2demand has a shortfall of 4000 Customer 3 demand of 4000 X is not satisfied