document.write( "Question 1155802: A plane with 150 seats may be chartered for$240 per person plus a fee of $6 per person for each empty seat. What number of passengers will provide the maximum income? \n" ); document.write( "

Algebra.Com's Answer #778455 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+n+\"$ = the number of filled seats
\n" ); document.write( "Let $\"+I+\"$ = the income
\n" ); document.write( "--------------------------------
\n" ); document.write( " $\"+I+=+240n+%2B+6n%2A%28+150+-+n+%29+\"$
\n" ); document.write( "This is:
\n" ); document.write( "[ Income ] = [ price/passenger x filled seats ] + [ cost/ empty seat x empty seats x filled seats ]
\n" ); document.write( " $\"+I+=+240n+%2B+900n+-+6n%5E2+\"$
\n" ); document.write( " $\"+I+=+-6n%5E2+%2B+1140n+\"$
\n" ); document.write( "The n-value of the peak is at:
\n" ); document.write( " $\"+-b%2F%282a%29+=+-1140+%2F+%28+2%2A%28-6%29%29+\"$
\n" ); document.write( " $\"+-b%2F%282a%29+=+95+\"$
\n" ); document.write( "95 passengers give the maximum income
\n" ); document.write( "---------------------------------------------
\n" ); document.write( "check:
\n" ); document.write( "The max income is:
\n" ); document.write( " $\"+I+=+240n+%2B+6n%2A%28+150+-+n+%29+\"$
\n" ); document.write( " $\"+I%5Bmax%5D+=+240%2A95+%2B+6%2A95%2A%28+150+-+95+%29+\"$
\n" ); document.write( " $\"+I%5Bmax%5D+=+22800+%2B+570%2A55+\"$
\n" ); document.write( " $\"+I%5Bmax%5D+=+22800+%2B+31350+\"$
\n" ); document.write( " $\"+I%5Bmax%5D+=+54150+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( "Here is the plot:
\n" ); document.write( " $\"+graph%28+500%2C+500%2C+-20%2C+200%2C+-6000%2C+60000%2C+-6x%5E2+%2B+1140x+%29+\"$
\n" ); document.write( "Looks like a match with my answer\r
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