Duck construction is supplying building materials for a new mall construction project in Oregon. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Duck's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered to be delivered by trucking, at least 40% of the total delivered to be delivered by railway, and up to 10% of the total delivered to be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons): Week Trucking Railway Air Cargo Limits Limits Limits 1 45 60 15 N 50 55 10 3 55 45 5 Costs ($ per 1000 tons) $200 $140 $500 The following is the LP model for this problem. The decision variables are shown in cells B3: D5. Cells E3:E5 and 36:38 are functions of the decision variables. Let Xij = amount shipped by mode i in weekj (thousands of tons) where i = 1(Truck), 2(Rail), 3(Air) and j = 1, 2, 3 WLij = weekly limit of mode i in weekj (as provided in above table, for example WL 12 = 50) MIN: 200(X11 + X12 + X13) + 140X21 + X22 + X23) + 500(X31 + X32 + X33) Subject to: Xij s WLij for all i andj mode Weekly limits by X11 + X12 + X13 + X21 + X22 + X23 + X31 + X32 + X33 2 250 Total required at end of three weeks Total required at end X11 + X21 + X31 + X12 + X22 + X32 2 200 of two weeks Total required at X11 + X21 + X31 120 end of first week Truck mix X11 + X12 + X13 2 0.45*250 requirement X21 + X22 + X232 0.40*250 Rail mix X31 + X32 + X33