Let xy - amount of units produced by plant node i for customer node j Max 96 V X11 + 102 V X12 + 96 V X13 V X14 102 V X21 + 90 V X22 - 84 V X23 114 7 X24 X3 1 X35 X33 X34 s.t. 1 V X11 + 1 V X12 + 1 V X13 + 1 V X14 5,000 1 V x21 + 1 V X22 + 1 V X23 + 1 V X24 X31 1 1 X32 + 1 V X23 + 1 V X34 5 4,000 Dummy 1 V x11 1 V X21 1 V X31 1 V X12 1 V X22 1 V X32 1 V X13 1 V X23 1 X33 1 V X14 1 V X24 xy 2 0 for all i, j Units Cost, $ Clifton Springs - Di O V O V Clifton Springs - Dz 16,000 X Clifton Springs - D3 O V O V Clifton Springs - D4 Danville - Di Danville - D2 o v O V Danville - D3 O V O V Danville - D4 Dummy - Di O V O V Dummy - D2 O V Dummy - D3 O V Dummy - D4 O V O V Total Cost 3,000 X Customer 2 v demand has a shortfall of 1000 Customer 3 v demand of 3000 v 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 D1 D2 DA Clifton Springs $96 $102 $96 $120 Danville $102 DES $84 $114 The plant capacities and customer orders are as follows: Plant Capacity (units) Distributor Orders (units) Clifton Springs 5000 D1 2000 D2 5000 Danville 3000 D:3000 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, enter "O". Note: Dummy origin has supply of 4000