document.write( "Question 1141780: The school musical will be held in a hall that has a seating capacity of 600. In the past, the musical committee has sold tickets for $10 each and tickets have always sold out.
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\n" ); document.write( "The committee is planning to increase the cost of the ticket price but they are concerned because they predict that for each $1 rise in the ticket price they will sell 25 less tickets. They have come to you for advice.
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\n" ); document.write( "Prepare an analysis summarising the relevant information for the committee with a recommendation for the new ticket price. The committee is also interested to know the expected increase in revenue
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Algebra.Com's Answer #762410 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+n+\"$ = the number of $1 increases in the ticket price
\n" ); document.write( "Their prediction is that $\"+600+-+25n+\"$ will be the number
\n" ); document.write( "of tickets they will sell at a price of $\"+10+%2B+n+\"$ dollars each
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\n" ); document.write( "Let $\"+R+\"$ = revenue from sales of tickets
\n" ); document.write( " $\"+R+=+%28+600+-+25n+%29%2A%28+10+%2B+n+%29+\"$
\n" ); document.write( "What value of $\"+n+\"$ gives them the maximum revenue?
\n" ); document.write( " $\"+R+=+6000+-+250n+%2B+600n+-+25n%5E2+\"$
\n" ); document.write( " $\"+R+=+-25n%5E2+%2B+350n+%2B+6000+\"$
\n" ); document.write( "The plot of $\"+R%28n%29+\"$ is a parabola with a maximum n-value at
\n" ); document.write( " $\"+-b%2F%282a%29+=+-350%2F%282%2A%28-25%29%29+\"$
\n" ); document.write( " $\"+-b%2F%282a%29+=+7+\"$
\n" ); document.write( "When $\"+n+=+7+\"$ , revenue is a maximum
\n" ); document.write( " $\"+R%7B7%7D+=+%28+600+-+25%2A7+%29%2A%28+10+%2B+7+%29+\"$
\n" ); document.write( " $\"+R%287%29+=+%28+600+-+175+%29%2A17+\"$
\n" ); document.write( " $\"+R%5B7%5D+=+425%2A17+\"$
\n" ); document.write( " $\"+R%287%29+=+7225+\"$
\n" ); document.write( "$7,225 is the maximum revenue they can make.
\n" ); document.write( "Revenue will increase for each $1 increase in ticket price
\n" ); document.write( "until the tickets cost $\"+10+%2B+7+=+17+\"$ $17
\n" ); document.write( "After that, Revenue will decrease.
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\n" ); document.write( "Here is the plot of ( n, R )
\n" ); document.write( " $\"+graph%28+600%2C+400%2C+-2%2C+15%2C+-1000%2C+10000%2C+-25x%5E2+%2B+350x+%2B+6000+%29+\"$ \r
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