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Braneast Airlines must determine how many airplanes should serve the Boston–New York–Washington air corridor and which flights to fly. Braneast may fly any of the daily flights shown in Table 36. The fixed cost of operating an airplane is $800/day. Formulate an MCNFP that can be used to maximize Braneast’s daily profits. (Hint: Each node in the network represents a city and a time. In addition to arcs representing flights, we must allow for the possibility that an airplane will stay put for an hour or more. We must ensure that the model includes the fixed cost of operating a plane. To include this cost, the following three arcs might be included in the network: from Boston 7 P.M. to Boston 9 A.M.; from New York 7 P.M. to New York 9 A.M.; and from Washington 7 P.M. to Washington 9 A.M.)
TAB LE 36 Leaves Arrives Flight Variable Cost City Time City Time Revenue of Flight (S) N.Y. 9 A.M. Wash. 10 A.M. $900 400 N.Y. 2 P.M. Wash. 3 P.M. $600 350 N.Y. 10 A.M. Bos. 11 A.M. $800 400 N.Y. 4 P.M. Bos. 5 P.M. $1,200 450 Wash. 9 A.M. N.Y. 10 A.M. $1,100 400 Wash. 3 P.M. N.Y. 4 P.M. $900 350 Wash. 10 A.M. Bos. 12 noon $1,500 700 Wash. 5 P.M. Bos. 7 P.M. $1,800 900 Bos. 10 A.M. N.Y. 11 A.M. $900 500 Bos. 2 P.M. N.Y. 3 P.M. $800 450 Bos. 11 A.M. Wash. 1 P.M. $1,100 600 Bos. 3 P.M. Wash. 5 P.M. $1,200 650
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