document.write( "Question 1156061: A store sells about 80 sweaters per month at a price of $ 30. For each $ 1 decrease in price, the store sells 5 more sweaters per month. Write a function that models this situation. Tell how the store can maximize monthly revenue. \n" ); document.write( "

Algebra.Com's Answer #778753 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+R+\"$ = monthly revenue
\n" ); document.write( "Let $\"+n+\"$ = number of $1 decreases in price
\n" ); document.write( "----------------------------------
\n" ); document.write( " $\"+R+=+%28+30+-+1%2An+%29%2A%28+80+%2B+5n+%29+\"$
\n" ); document.write( " $\"+R+=+2400+-+80n+%2B+150n+-+5n%5E2+\"$
\n" ); document.write( " $\"+R+=+-5n%5E2+%2B+70n+%2B+2400+\"$
\n" ); document.write( "The n-value of the peak is at:
\n" ); document.write( " $\"+n%5Bmax%5D+=+-b%2F%282a%29+\"$
\n" ); document.write( " $\"+n%5Bmax%5D+=+-70%2F%28+2%2A%28-5%29%29+\"$
\n" ); document.write( " $\"+n%5Bmax%5D+=+7+\"$
\n" ); document.write( "-----------------------
\n" ); document.write( "If the store lowers the price by $7, the
\n" ); document.write( "monthly revenue will be maximum
\n" ); document.write( "---------------------------------------
\n" ); document.write( "Here's the plot of $\"+R+\"$ and $\"+n+\"$ :
\n" ); document.write( " $\"+graph%28+500%2C+500%2C+-2%2C+20%2C+-300%2C+3000%2C+-5x%5E2+%2B+70x+%2B+2400+%29+\"$
\n" ); document.write( "The maximum revenue is:
\n" ); document.write( " $\"+R%5Bmax%5D+=+%28+30+-+1%2A7+%29%2A%28+80+%2B+5%2A7+%29+\"$
\n" ); document.write( " $\"+R%5Bmax%5D+=+23%2A115+\"$
\n" ); document.write( " $\"+R%5Bmax%5D+=+2645+\"$
\n" ); document.write( "$2,645 \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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