In a humanitarian mission, cargo needs 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 airplanes $($Table $1).$ There is a tradeoff between the

range of an airplane and the amount of fuel and cargo the airplane takes. In general, the range of

an airplane is shorter if the airplane takes more cargo or less fuel. Figures $1-3$ show piecewise

linear functions of cargo payload for the three types of airplanes in Table $1.$

Table $2$ shows the distances between eight airports. There are three C$-5$A$,$ three C$-17,$ and three

$KC-10$ airplanes available at the airport XDAT. Cargo is pre$-$staged at two POEs, AVXV and

BAEY, and must be shipped to the POD, FUQN. Airplanes fly from XDAT to AVXV or BAEY

to pick up cargo, and then ship them to FUQN. Each airplane may make at most one trip from

XDAT to FUQN. Please help the planner find a logistics plan that maximizes the total amount of

cargo shipped to FUQN.

Table $1.$ Airplane Types.

Figure $1.$ A Piecewise Linear Function of C$-5$A Cargo Payload.

$350000$

$$

Figure $3.$ A Piecewise Linear Function of KC$-10$ Cargo Payload.

Table $2.$ Distances $($Miles$)$ between Airports.