Question 1155802
Let {{{ n }}} = the number of filled seats
Let {{{ I }}} = the income
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{{{ I = 240n + 6n*( 150 - n ) }}}
This is:
[ Income ] = [ price/passenger x filled seats ] + [ cost/ empty seat x empty seats x filled seats ]
{{{ I = 240n + 900n - 6n^2 }}}
{{{ I = -6n^2 + 1140n }}}
The n-value of the peak is at:
{{{ -b/(2a) = -1140 / ( 2*(-6)) }}}
{{{ -b/(2a) = 95 }}}
95 passengers give the maximum income
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check:
The max income is:
{{{ I = 240n + 6n*( 150 - n ) }}}
{{{ I[max] = 240*95 + 6*95*( 150 - 95 ) }}}
{{{ I[max] = 22800 + 570*55 }}}
{{{ I[max] = 22800 + 31350 }}}
{{{ I[max] = 54150 }}}
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Here is the plot:
 {{{ graph( 500, 500, -20, 200, -6000, 60000, -6x^2 + 1140x ) }}}
Looks like a match with my answer