SOLUTION: Hello,the problem I'm trying to solve is,
"A plane with a capacity of 120 passengers is to be chartered for an excursion. The price of one ticket is to be $60 if 100 people or f
Algebra.Com
Question 683794: Hello,the problem I'm trying to solve is,
"A plane with a capacity of 120 passengers is to be chartered for an excursion. The price of one ticket is to be $60 if 100 people or fewer buy tickets. The airline will reduce the price of every ticket by 50 cents for each ticket sold over 100. How many additional passengers over 100 will bring about maximum income?"
I know the first part of the equation will probably be (120 + 100x), but I'm not to sure about the rest of the equation which I need in order to graph the parabola. Help would be greatly appriciated. Thanks.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
the income will go up for each passenger until the one, where the income would be $
after that, evidently, the next passenger would pay only $, and the other passengers would also pay $ less
let's put that in equation:
where "" is the number of passenger
note that this equation applies only for "" or to
the is the bit that takes away cents for each passenger above the ; and the "" is the number of passenger
A bit of algebra turns the income equation to
Now, we want to maximize the income. Calculus to the rescue, as the local maximum implies that the derivative of the equation equals zero.
The derivative of the equation is
If we put this equal to zero, then has to be .
That is thus the number of passengers that income.
Plugging into the income equation means that said income would be
$.
And we can easily verify that this is indeed the , by seeing what the income would be for passengers (it would be $) and passengers ($ also).
RELATED QUESTIONS
i need help to do this fraction
An airplane has a 200 seat capacity and is to be... (answered by stanbon)
Hello, can someone please help me on this question.
A railway company charge... (answered by Mlallory_Pl)
An airline is flying from Los Angeles to Albuquerque and making a stop in Phoenix. A... (answered by josmiceli)
What am I supposed to do if a question is like this. A school bus with capacity for 42... (answered by nerdybill)
A plane with 150 seats may be chartered for$240 per person plus a fee of $6 per person... (answered by josmiceli)
Suppose that the probability that a passenger will miss a flight is 0.0999. Airlines do... (answered by ikleyn)
A one-plane airline has a passenger capacity of 120. The number of passengers on a... (answered by jim_thompson5910)
students of a class go for an excursion the total expending for food is Rs480.
8... (answered by Maths68)
A train fare for a School child is half the fare for a teacher. The total fare for 120... (answered by josgarithmetic)