An airline is preparing to replace its old planes with three new styles of

jets. The airline needs $17$ new planes to service its current routes. The decision regarding which planes

to purchase should balance cost with capability factors, including the following: $(1)$ The airline can

finance up to $$700$ million in purchases; $(2)$ each $7$A$7$ jet will cost $$38$ million, each $7$B$7$ jet will cost $$27$

million, and each $7$C$7$ jet will cost $$22$ million; $(3)$ at least one$-$third of the planes purchased should be

the longer$-$range $7$A$7$; $(4)$ the annual maintenance budget is to be no more than $$12$ million; $(5)$ the

annual maintenance cost per $7$A$7$ is estimated to be $$800,000,$ $$600,000$ for each $7$B$7,$ and $$500,000$ for

each $7$C$7$; and $(6)$ annually, each $7$A$7$ can carry $125,000$ passengers, each $7$B$7$ can fly $95,000$ passengers,

and each $7$C$7$ can fly $80,000$ passenger