(ii) linear programming formulation Let xij= number of units i shipped to client j, using the indices from the given table. (It may be necessary to combine plants or distributors in a single node in order to solve this problem. Use index number 5 for this type of node. Enter "DNE" in any unused answer blanks.) Max s.t. Orders from Clifton Springs Orders from Danville Orders from/for Dummy Node Orders for D1 Orders for D2 Orders for D3 Orders for D4 x11+x12+x13+x145000 x21+x22+x23+x243000 x31+x32+x33+x344000 x11+x21+x31=2000 x12+x22+x32=5000 x13+x23+x33=3000 x14+x24+x34=2000 xij0foralli,j. b) How many units should each plant produce for each customer to maximize profits? Optimal Solution (b) How many units should each plant produce for each customer to maximize profits? Optimal Solution (c) Which customer demands will not be met? Distributor 1 will have a shortfall of Distributor 2 will have a shortfall of Distributor 3 will have a shortfall of Distributor 4 will have a shortfall of units. units. units. units. 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 productio 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. The plant capacities and customer orders are as follows. (a) Develop a network model and a linear programming formulation of this problem. (i) network model (Submit a file with a maximum size of 1MB. ) No file chosen This answer has not been graded yet