In a humanitarian mission, cargos need to be shipped in airplanes from a point of embarkation (POE) to a point of debarkation (POD). A logistics planner designs a plan to ship cargos from two POES to one POD using three types of aircraft (Table 5). There is a tradeoff between the range of an aircraft and the amount of fuel and cargos the aircraft takes. In general, the range of an aircraft is shorter if the aircraft takes more cargos or less fuel. Figures 1-3 show piecewise linear functions of cargo payload for the three types aircraft in Table 5. Table 6 shows the distances between eight airports. There are one C-5A, one C-17, and one KC- 10 aircraft available at the airport XDAT. Suppose a total of 841,299 lb cargos may be pre- staged at two airports, AVXV and TMKH, and must be shipped to the airport FUQN. Please help the planner find a logistics plan that minimizes the total flight distance. Table 5. Aircraft types. Maximum Maximum Aircraft Payload Fuel Load Range Range Maximum Range (miles) (miles) (miles) Cargo Payload Maximum Payload with Door Cargo Maximum Fuel Door Height Width (inches) (inches) (lb) (lb) Cargo Bay MOG Length Equivalent Kinches) Upload Refuel Download Time Time Time (hours) (hours) (hours) C-SA C-17 1500 3500 2250 4500 4000 6000 KC-10 3250 5500 456500 303429 7000 242000 380000 162 228 1736 T 3.75 3.25 3.25 253325 148 216 1022 3 $ 1.5 3 221580 98 140 1308 1.2 2.25 2.25 2.25 Range (miles) Figure 3. A Piecewise Linear Function of KC-10 Cargo Payload. Table 6. Distances (miles) between airports. XDAT AVXV BAEY BPWZ HNTK TMKH YWHG FUQN XDAT 0 2697 7240 4773 1728 5820 5332 13101 AVXV 2697 0 1703 2851 1040 3148 3621 6058 BAEY 7240 1703 0 1722 278 3715 3671 6244 BPWZ 4773 2851 1722 0 2726 2419 2787 3013 HNTK 1728 1040 278 2726 0 3399 1000 3068 TMKH 5820 3148 3715 2419 3399 0 5140 2034 YWHG 5332 3621 3671 2787 1000 5140 0 2920 FUQN 13101 6058 6244 3013 3068 2034 2920 0