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Mathematics / Economic

11/24/2011 5:31 AM

A club makes plan for a charter flight for her christian members on a trip to Jerusalem. The plan round trip fare is 800 per person if at least 100 people go and will decrease by 25 for every additional person above the minimum of 100 to go. Find the number of passengers that will maximize the revenue.

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Guru
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#1

Re: Mathematics / Economic

11/24/2011 5:46 AM

Arrrrroooooooooooogah! Homework alarm! Arrrooooooooooooooogah!

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#2

Re: Mathematics / Economic

11/24/2011 5:53 AM

What about the Atheists who want to visit Jerusalem?
Del

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#3

Re: Mathematics / Economic

11/24/2011 6:19 AM

This sounds like a linear programming exercise from Junior School (that's 7 - 11 yo in the UK).

Anyway, this question can not be answered, because we don't know whose revenue is to be maximised and what their profit margin is.

Are you telling us this nice Christian lady is going to pocket the 25 difference if more than 100 people go?

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#4

Re: Mathematics / Economic

11/24/2011 6:21 AM

Do you leave Abe behind to look after the business and maximize the revenue?

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#5

Re: Mathematics / Economic

11/24/2011 6:26 AM

The way I see it, if 200 people go the last person gets paid 1,700 for going ( 800 - (100x25) ).
Note to self, be sure to book late.
Del
(Not sure if Atheist cats are allowed)

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#6

Re: Mathematics / Economic

11/24/2011 7:06 AM

If maximum revenue is what is wanted, then a full plane is the answer.

If maximum revenue means greatest profit (no pun intended) per person, then 100 or less flyers is the answer.

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#8
In reply to #6

Re: Mathematics / Economic

11/24/2011 8:05 AM

or fewer.

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#7

Re: Mathematics / Economic

11/24/2011 8:05 AM

You're too young to travel alone. Go ask your mother.

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#9

Re: Mathematics / Economic

11/24/2011 10:16 AM

Passenger 131 will pay 25

passenger 132 will go free

The revenue will be equal for 131 and 132

So make it 132 and give someone a free trip - the Jerusalem crowd will see to it that he will be relieved of the 800 xxx he saved by being last.

If the rest of the seats are filled by normal paying people the maximum revenue will be at 100 club members .

The person who made the stupid offer should be fired.

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#10

Re: Mathematics / Economic

11/24/2011 10:27 AM

Will this be an international flight?

Del, take note:

Traveling Internationally?

If traveling with your pet internationally, then you should attach an extra copy of your pet's health certificate to the container.

From:

Pet Cargo Travel - Pet airline Cargo Crates - PetTravel.com

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#11

Re: Mathematics / Economic

11/24/2011 10:31 AM

Yes.

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#12

Re: Mathematics / Economic

11/24/2011 11:22 AM

Would it be greener if they went by bus?

[This one might out-do the Bath Breaking Thread!]

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#13
In reply to #12

Re: Mathematics / Economic

11/24/2011 11:31 AM

One of these?... Looks pretty green to me.

Del

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#18
In reply to #13

Re: Mathematics / Economic

11/24/2011 1:48 PM

Just my era....drool

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#14

Re: Mathematics / Economic

11/24/2011 11:32 AM

Thank you for your contributions. Since this problem is mathematics/Economics I would think we can approach it as follows: The total amount the minimum passengers number of 100 pay @ 800 each = 80000 Each additional passenger pays 25 less than the previous passenger that is: The 101th passenger pays 775 i.e 800-25. The 102th passenger pays 750 i.e 775-25 and so on. However, this progression will reach a limiting value of zero. That is: 80000+ sum[800-25n] for n taken values from 1, 2, .... . Where n final value is what make the parentheses zero. That analysis make our n to have a terminal value of 32. Thus the total passenger is = 132 and total passenger payment is 92,400 as the maximum revenue . Have a great day!

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#15
In reply to #14

Re: Mathematics / Economic

11/24/2011 11:50 AM

You too!

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#16
In reply to #14

Re: Mathematics / Economic

11/24/2011 1:02 PM

However, this progression will reach a limiting value of zero.

That is not stated in the question, andzero is not a mathematical limit.
Del

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#17

Re: Mathematics / Economic

11/24/2011 1:42 PM

The club got greedy and overbooked as many as they could to maximise profits. Unfortunately this led to 300 people trying to get on the chartered flight designed only for 220 (the charter's fine print did not say anywhere that one or more people could'nt travel for free). A quick bribe to the charter company (again to maximise profits) and all 300 people were on their way.

Tragedy struck when the overloaded flight failed to clear a mountain resulting in the deaths of everyone on board.

Welcome to the real world where situations similar to this happen and big business is put before the safety of consumers (sometimes with tragic results).

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