Question

An airline finds that if it prices a cross-country ticket at $300, it will sell 400 tickets per day. It estimates that each $10 price reduction will result in 50 more tickets sold per day. Find the ticket price (and the number of tickets sold) that will maximize the airline's revenue.

Answer 1

price = $190

quantity = 950 tickets

Explanation:

revenue = price * quantity

n = number of $10 price reductions

price = 300 - 10n

quantity = 400 + 50n

r = (300 - 10n)(400 + 50n)

recognize these as the factors of a quadratic that opens down

the vertex will therefor be the maximum revenue

the roots are:

300 - 10n = 0

300 = 10n

n = 30

400 + 50n = 0

50n = -400

n = -8

vertex is at mid point of the roots

n = (-8 + 30)/2

n = 11

price = 300 - 10n

price = 300 - 10(11)

price = 190

quantity = 400 + 50n

quantity = 400 + 50(11)

quantity = 950