LeapFrog Airways Provides Passenger Service for Indianapolis,Baltimore,Memphis,Austin,and Tampa

Essay

LeapFrog Airways provides passenger service for Indianapolis,Baltimore,Memphis,Austin,and Tampa.LeapFrog has two WB828 airplanes,one based in Indianapolis and the other in Baltimore.Each morning the Indianapolis based plane flies to Austin with a stopover in Memphis,and the Baltimore based plane flies to Tampa with a stopover in Memphis.Both planes have a coach section with a 120-seat capacity.
LeapFrog uses two fare classes: a discount fare D class and a full fare F class.Leapfrog's products,each referred to as an origin destination itinerary fare (ODIF),are listed below with their fares and forecasted demand.
Develop a linear programming model for LeapFrog's problem situation and determine how many seats LeapFrog should allocate to each ODIF.
$$\begin{array} { l l l l l l l } \text { ODIF } & \text { Origin } & \text { Destination } & \text { Fare Class } & \text { ODIF Code } & \text { Fare } & \text { Demand } \\\hline 1 & \text { Indianapolis } & \text { Memphis } & \text { D } & \text { IMD } & 175 & 44 \\2 & \text { Indianapolis } & \text { Austin } & \text { D } & \text { IAD } & 275 & 25 \\3 & \text { Indianapolis } & \text { Tampa } & \text { D } & \text { ITD } & 285 & 40 \\4 & \text { Indianapolis } & \text { Memphis } & \text { F } & \text { IMF } & 395 & 15 \\5 & \text { Indianapolis } & \text { Austin } & \text { F } & \text { IAF } & 425 & 10 \\6 & \text { Indianapolis } & \text { Tampa } & \text { F } & \text { ITF } & 475 & 8 \\7 & \text { Baltimore } & \text { Memphis } & \text { D } & \text { BMD } & 185 & 26 \\8 & \text { Baltimore } & \text { Austin } & \text { D } & \text { BAD } & 315 & 50 \\9 & \text { Baltimore } & \text { Tampa } & \text { D } & \text { BTD } & 290 & 42 \\10 & \text { Baltimore } & \text { Memphis } & \text { F } & \text { BMF } & 385 & 12 \\11 & \text { Baltimore } & \text { Austin } & \text { F } & \text { BAF } & 525 & 16 \\12 & \text { Baltimore } & \text { Tampa } & \text { F } & \text { BTF } & 490 & 9 \\13 & \text { Memphis } & \text { Austin } & \text { D } & \text { MAD } & 190 & 58 \\14 & \text { Memphis } & \text { Tampa } & \text { D } & \text { MTD } & 180 & 48 \\15 & \text { Memphis } & \text { Austin } & \text { F } & \text { MAF } & 310 & 14 \\16 & \text { Memphis } & \text { Tampa } & \text { F } & \text { MTF } & 295 & 11 \\\hline\end{array}$$