7. UPak is a subsidiary of an LTL (Iess-than-truck-load) transportation company. Customers bring their shipments to the UPak terminal to be loaded on the trailer and can rent space up to 36 ft. The customer pays for the exact linear space (in foot increments)

the shipment occupies. No partial shipment is allowed, in the sense that the entire shipment per customer must be on the same trailer. A movable barrier, called bulkhead, is installed to separate different shipments. The per-foot fee UPak collects depends on the destination of the shipment:The longer the trip, the higher the fee. The following table provides the outstanding orders UPak needs to process.

Order 1 Size (it) 5 Rate ($) 120 2 3 11 22 93 70 4 5 6 15 7 9 85 125 104 7 8 18 14 98 130 9 10 10 12 140 65 The terminal currently has two trailers ready to be loaded. Detennine the priority orders that will maximize the total income from the two trailers. (Hint A formulation using binary xij to represent load i on trailer j is straightforward. However, you are challenged to define Xij as feet assigned to load i in trailer j. The use if-then constraint to prevent partial load shipping.)