Question

Let q = demand for seats on a 500-seat airplane and p = price charged per ticket. Suppose that q = 600 - 3p and assume that the unit cost of flying a passenger is $50. To maximize profit from the flight, the airline should charge how much per ticket?

Answer 1

$125

Explanation:

Given the equation q = 600 - 3p where;

q = demand for seats on a 500-seat airplane

p = price charged per ticket

Revenue = demand for seats * price charged per ticket i.e pq

Revenue = p * 600 - 3p ... 1

Cost of flying a passenger = unit cost * demand for seats = 50q

Cost of flying a passenger = 50q ...2

Profit generated will be the revenue less cost i.e Revenue - cost

Profit generated = p(600 - 3p) - 50q

= p(600 - 3p) - 50(600-3p)

= 600p-3p²-30000+150p

= -3p²+750p-30000

Profit P = -p²+250p-10000

To maximize the profit, dP/dp = 0

-2p+250 = 0

-2p = -250

p = $125

To maximize profit, the airline should charge $125 per ticket