"Guess who" <email@example.com> wrote in message news:firstname.lastname@example.org... > On Tue, 15 Feb 2005 04:49:05 GMT, "Darrell" <email@example.com> > 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.