Answer:
The maximum revenue is $661,250.
Step-by-step explanation:
The total revenue (R) is the product between the number of passengers (N) and the price of each ticket (P), so the inicial revenue is:
R = N * P = 8000 * 70 = $560,000
For each 1$ increase in the ticket, the airline loses 50 passengers, so if we call "x" the increase in the ticket price, we have that the revenue equation will be:
R = (8000-50*x) * (70+x) = 560000 + 8000*x - 50*70*x -50x2
R = -50*x2 + 4500*x + 560000
The value of x that gives the maximum value of a quadratic function is found using the formula:
x = -b/2a
where a and b are coefficients of the quadratic equation (in our case, a = -50 and b = 4500)
So the value of x that gives the maximum revenue is:
x = -4500 / (-100) = 45
Using this value in the revenue equation, we have that the maximum R is:
R = -50*45^2 + 4500*45 + 560000 = $661,250
(To get this revenue, the ticket will cost 70+45 = $115 and there will be 8000-50*45 = 5750 passengers)
