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 Plant Distributor Orders (units) Clifton Springs D1 2,000 Danville 3,000 DZ 5,000 D3 3,000 D4 2,000 (ii) linear programming formulation Let x = number of units / 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 32 .x1 + 34 .x12+ 32 . X13 + 40 . x14 + 34 . x21 + 30 . X22 + 28 . X23 + 38 .X24 s.t. Orders from Clifton Springs X11 + X12 + * 13 + * 143 5000 Orders from Danville *21 + X22 + X23 + X24