An airline sells all the tickets for a certain route at the same price. If it charges 200 dollars per ticket i?
An airline sells all the tickets for a certain route at the same price. If it charges 200 dollars per ticket it sells 10,000 tickets. For every 15 dollars the ticket price is reduced, an extra thousand tickets are sold. Thus if the tickets are sold for 185 dollars each then 11,000 tickets sell. It costs the airline 100 dollars to fly a person.(a) Express the total profit P in terms of the number n of tickets sold.
(b) Express the total profit P in terms of the price p of one ticket.
200 dollars sells 10,000 tickets.
200-15n = price of a ticket
10,000+1000n = persons
-(10,000+1000n)*100=cost of flying
(200-15n)*(10,000+1000n) = total profit before considering cost of flying
(200-15n)*(10000+1000n)-(10000+1000n)*100n = earned money
so…
(200-115n)*(10000+1000n)=earned money
factor it and it’ll be
2,000,000-950000n-115000n^2 =P
in terms of the price p of 1 ticket, we just replace n with 200-15p
2,000,000-950000(200-15n)-115000(200-15n)^2
2,000,000-190,000,000+14,250,000p-4,600,000,000-25,875,000p^2+690,000,000p
which = -4,788,000,000 + 704,250,000p-25,875,000p^2 =P
I think.
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