1. If exactly 170 people sign up for a charter airplane flight, the Leisure Worl
ID: 3198813 • Letter: 1
Question
1. If exactly 170 people sign up for a charter airplane flight, the Leisure World Travel Agency charges $390 per person. However, if more than 170 people sign up for the flight, then each fare is reduced by $1.50 for each additional person beyond 170. Thus, if 174 people sign up, the fare for every passenger is reduced by $6 (4 times $1.50) and so each fare would be $384. Let x represent the number of passengers on the airplane. Find a function p(x) that expresses the price each person pays as a function of the number of passengers on the airplane. Explain what you are doing and include the units of your function. a. b. Find a function Ree) that expresses the revenue that Leisure World Travel Agency will receive as a function of the number of passengers on the airplane. doing and include the units of your function. Explain what you are How many passengers will produce maximum revenue for Leisure World. Do this problem in two different ways: c. i. Using algebra techniques from the first part of the course. Explain what you are doing. ii. Using calculus techniques from the second half of the course. Explain what you are doing. How do you know you have a maximum? d. How much will each passenger pay? e. How much revenue will Leisure World earn? This part is extra credit, and will only be awarded if it is perfect. You'll need to explain what you are doing. Using the concept of elasticity, find the price that produces unit elasticity. This should be the same answer you got in part d, because the unit elastic price produces maximum revenue. f.Explanation / Answer
Solved the first five parts with additional sub-parts as per Chegg guidelines, the question f part is too big and requires a lot of explanation, post one more question to get this answer as per Chegg guidelines
a) Let the number of passengers greater than 170 be x
Then for each passenger, the price reduction in ticket is equal to 1.5$
p(x) = 390 - 1.5x
The units of p(x) will be equal to dollars and we are basically assuming the number of people more than 170 by a variable x then estimating the fare
b)
Revenue = (Number of passengers) * (Price of ticket)
=> (170+x) * (390-1.5x)
The units for the same will be dollars and we are basically modifying the passengers to (170+x), where x is the extra number of people over 170
c)
(i) R(x) = (170+x) * (390-1.5x)
R(x) = -1.5x^2 + 135x + 66300
I don;t know what techniques, you have learn but in our case, we have learned that maxima occurs at coefficient of b/(2*coefficient of a)
which gives x = 135/3 = 45
b) Using calculus
R(x) = -1.5x^2 + 135x + 66300
R'(x) = -3x + 135
Equating the derivative to zero, we get x = 45, which is similar to above answer
d)
Price per passenger = (390-1.5x) = (390 - 1.5(45)) = 322.5$
e) Revenue earned by Leisure world
=> (170+x)(390-1.5x)
=> (170+45)*(322.5)
=> 69337.5$
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