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Darrell
Posts:
251
Registered:
12/6/04


Re: Max. Income, Quadratic Equation
Posted:
Feb 16, 2005 12:22 AM


"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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