Problema Solution
If exactly 200 people sign up for a charter flight,Fun Times Travel Agency charges $300/person. However, if more than 200 people sign up for the flight(assume that this is indeed the case),then each fare is reduced by $1 for each additional person. Determine the number of passengers that will maximize revenue for the travel agency. What is the maximum revenue? What will be the fare per passenger in this case?
Answer provided by our tutors
Let x represent the number of passengers then the revenue is:
R(x) = 300*200 + ((x - 200)/2)(199 + (199 + (x - 200 - 1)*(-1))
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click here to see the step by step simplification
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R(x) = (1/2)(-x^2 + 799x + 200)
We need to maximum of R(x)
Since the quotient in front of x^2 is -1 <0 the function R(x) has maximum
R max = c - b^2/(4a)
a = (-1/2)
b = -799/2
c = 200/2
c = 100
R max = 100 - (-799/2)^2/(4*(-1/2))
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click here to see the step by step calculation
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R max = $79,900.13 is the maximum revenue.
x = -b/2a
x = (-799/2)/(2*(-1/2))
x = 400 passengers will maximize revenue.
The average fare per person will be 79,900.13/400 = $199.75.