An airline runs daily flights from Alaska to Canada. When the airline charges $4

Question

An airline runs daily flights from Alaska to Canada. When the airline charges $400 per ticket, 24 people fly. Each $10 the fare is increased, 1 fewer person flies. Conversely, each $10 the fare is lowered, 1 more person flies.

(a) Let c denote the cost charged for each ticket, let T(c) be the number of tickets sold, and let R(c) be the revenue. Write down formulas for T(c) and R(c).
(b) How much should the airline charge per ticket to maximize total revenue?
(c) Suppose that the airliner's airplanes can only seat 30 people. Write down an inequality involving T(c) that represents this, and deduce a corresponding inequality for c.
(d) Does the condition in (c) change the answer for (b), and if so, what is the new answer? Explain.

Explanation / Answer

T(c) = 400+10 x

R(c) = (400+10x)(24-x)

R'= -(400+10x)+(24-x)10

R"= -10-10<0

Set R'=0

24-x = 40+x

2x= -16

x=-8

Ticket cost = 320

and no of persons =8

d) does not change

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