For a particular flight from Dulles to SF, an airline uses wide-body jets with a capacity of 460 passengers. It costs the airline $4,000 plus $60 per passenger to operate each flight. Through experience the airline has discovered that if a ticket price is $T, then they can expect (460−1.T) passengers to book the flight. Determine the ticket price, T, that will maximize the airline's profit.

Answer:$ 260Step-by-step explanation:GivenInitially 460 passenger travels It cost $ 4000 +$60 per passenger If ticket Price is $ Tthen they expect 460-T passengers Total Revenue generated by tickets[tex]=T\times (460-T)[/tex]cost to airlines [tex]=4000+60\times (460-T)[/tex]Profit is [tex]=T\times (460-T)-4000-60\times (460-T)[/tex][tex]P=(460-T)(T-60)-4000[/tex]To get maximum Profit differentiate P w.r.t to T and Equate it to zero[tex]\frac{\mathrm{d} P}{\mathrm{d} T}=\frac{\mathrm{d} }{\mathrm{d} (460-T)(T-60)T}-0[/tex][tex]\frac{\mathrm{d} P}{\mathrm{d} T}=-T+60+460-T=0[/tex][tex]520=2T[/tex][tex]T=260[/tex]Therefore it cost $ 260 to get maximum Profit