document.write( "Question 453695: an art museum charges $10 for an adult admission. The museum estimates they will lose 15 adult visitors per day for each one dollar increase in price. If the museum averages 300 adult visitors a day, which is the most profitable adult admission price? \n" ); document.write( "

Algebra.Com's Answer #311696 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+M+\"$ = money taken in
\n" ); document.write( "Let $\"+i+\"$ = number of $1 increases
\n" ); document.write( "Money in = (number of adult visitors) x (admission per visitor)
\n" ); document.write( " $\"+M+=+%28+300+-+15i+%29%2A%28+10+%2B+i+%29+\"$
\n" ); document.write( " $\"+M+=+3000+-+150i+%2B+300i+-+15i%5E2+\"$
\n" ); document.write( " $\"+M+=+-15i%5E2+%2B+150i+%2B+3000+\"$
\n" ); document.write( " $\"+M+=+-i%5E2+%2B+10i+%2B+200+\"$
\n" ); document.write( "The maximum money in occurs at $\"+i+=+-b%2F%282a%29+\"$
\n" ); document.write( "where the equation has the form $\"+f%28x%29+=+a%2Ax%5E2+%2B+bx+%2B+c+\"$
\n" ); document.write( " $\"+a+=+-1+\"$
\n" ); document.write( " $\"+b+=+10+\"$
\n" ); document.write( " $\"+i%5Bmax%5D+=+-10%2F%282%2A%28-1%29%29+\"$
\n" ); document.write( " $\"+i%5Bmax%5D+=+5+\"$
\n" ); document.write( " $\"+10+%2B+i+=+10+%2B+5+\"$
\n" ); document.write( " $\"+10+%2B+i+=+15+\"$
\n" ); document.write( "The most profitable admission price is $15/visitor \n" ); document.write( "

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