Question

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 1

Answer:$ 260

Step-by-step explanation:

Given

Initially 460 passenger travels

It cost $ 4000 +$60 per passenger

If ticket Price is $ T

then they expect 460-T passengers

Total Revenue generated by tickets$=T\times (460-T)$

cost to airlines $=4000+60\times (460-T)$

Profit is $=T\times (460-T)-4000-60\times (460-T)$

$P=(460-T)(T-60)-4000$

To get maximum Profit differentiate P w.r.t to T and Equate it to zero

$\frac{\mathrm{d} P}{\mathrm{d} T}=\frac{\mathrm{d} }{\mathrm{d} (460-T)(T-60)T}-0$

$\frac{\mathrm{d} P}{\mathrm{d} T}=-T+60+460-T=0$

$520=2T$

$T=260$

Therefore it cost $ 260 to get maximum Profit