An airline operates a fleet of 15 jet aircraft, all equipped with the JET32 engine. The airline performs its own engine-related repairs and maintenance at its repair facility. The maintenance director is reviewing the spare parts ordering and stocking policy for the next three years. The JET32 engine consists of 4 main modules, A, B, C, and D. When planes come in for repairs, sometimes the entire engine must be replaced because of extensive damage and wear. More often, however, only certain modules need replacement. The following table 1 contains the forecasted requirements for individual engine modules and complete engines for the next 3 years. The airline places orders for complete engines and modules at the beginning of the year with JET Inc., the manufacturer of the JET32 engine. The following table 2 shows the projected prices for engines and modules the JET Inc. might charge in the next three years. Note that complete engine cost less than the total cost of buying one module of each type. Assume that the cost of cannibalizing, i.e., breaking a complete engine into four individual modules, is negligible compared to the cost of these modules. The mix of engines and modules the airline orders from JET Inc. must, therefore, account for the economies in ordering complete engines. Assuming that the airline does not have any inventory of modules or engines in hand, formulate an integer programming problem to determine the order quantities for the next 3 years, while minimizing the total cost of purchases. Assume that there are no inventory carrying costs.

Year Module A Module B Module CModule D Complete engine 4 0 4 Table 1: Forecasted engine/module requirements Year Module A Module B Module CModule D Complete engine 5.0 5.5 6.0 Table 2: forecasted engine/module prices. 0.5 0.6 0.7 2.0 2.2 2.5 7.8 7.5 7.0