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Topic: Max. Income, Quadratic Equation
Replies: 3   Last Post: Feb 16, 2005 12:22 AM

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Darrell

Posts: 251
Registered: 12/6/04
Re: Max. Income, Quadratic Equation
Posted: Feb 16, 2005 12:22 AM
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"Guess who" <notreally.here@here.com> wrote in message
news:pir411duki4dm1ukkqovoaak6cqov7m2gk@4ax.com...
> On Tue, 15 Feb 2005 04:49:05 GMT, "Darrell" <dr6583@comcastsnip.net>
> wrote:
>

>>>> A plane with 100 seats may be chartered for $200 per person plus a fee
>>>> of $5 per person for each empty seat. What number of passengers will
>>>> provide the maximum income?

>
>>> Let p be the number of passengers and i the income then
>>>
>>> i = p*200 + p*(100 - p)*5
>>> = 700*p - 5p^2
>>>
>>> and you need to maximize i. Note that it makes no sense to
>>> differentiate i wrt p because neither is a continuous variable.

>>
>>That doesn't matter; for all intents and purposes the problem can be
>>modelled by this (continuous) function.

>
> Agreed. Any problem in misunderstanding can be avoided if algebra
> [completing the square] is used instead in this instance.


I'm not sure I get your point. Using algebra "instead" of calculus in this
instance has nothing to do with whether or not the function is continuous.
The poster I was responding to apparently is concerned about the continuity
(I assume since the feasible domain is integers between 0 and 100.) Please
elaborate as to your point.

--
Darrell



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