document.write( "Question 534954: The manager of a large apartment complex knows from experience that 120 units will be occupied if the rent is 368 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 4 dollar increase in rent. Similarly, one additional unit will be occupied for each 4 dollar decrease in rent. What rent should the manager charge to maximize revenue? \n" ); document.write( "

Algebra.Com's Answer #351719 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"n\"$ = number of $4 in rent ( up or down )
\n" ); document.write( "Let $\"+R+\"$ = manager's revenue
\n" ); document.write( "For increase in rent:
\n" ); document.write( " $\"+R+=+%28+120+-+n+%29%2A%28+368+%2B+4n+%29+\"$
\n" ); document.write( " $\"+R+=+44160+-+368n+%2B+480n+-+4n%5E2+\"$
\n" ); document.write( " $\"+R+=+-4n%5E2+%2B+112n+%2B+44160+\"$
\n" ); document.write( " $\"+R%2F4+=+-n%5E2+%2B+28n++%2B+11040+\"$
\n" ); document.write( "and, for decrease in rent:
\n" ); document.write( " $\"+R+=+%28+120+%2B+n+%29%2A%28+368+-+4n+%29+\"$
\n" ); document.write( " $\"+R+=+44160+%2B+368n+-+480n+-+4n%5E2+\"$
\n" ); document.write( " $\"+R+=+-4n%5E2+-112n+%2B+44160+\"$
\n" ); document.write( " $\"+R%2F4+=+-n%5E2+-+28n+%2B+11040+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "For rent increase,
\n" ); document.write( " $\"+n%5Bmax%5D+=+-%2828%2F%28-2%29%29+\"$
\n" ); document.write( " $\"+n%5Bmax%5D+=+14+\"$
\n" ); document.write( " $\"+R%2F4+=+-14%5E2+%2B+28%2A14++%2B+11040+\"$
\n" ); document.write( " $\"+R%2F4+=+-196+%2B+392+%2B+11040+\"$
\n" ); document.write( " $\"+R%2F4+=+11236+\"$
\n" ); document.write( "----------------
\n" ); document.write( "For rent decrease,
\n" ); document.write( " $\"+n%5Bmax%5D+=+-%28-28%29%2F%28-2%29%29+\"$
\n" ); document.write( " $\"+n%5Bmax%5D+=+-14+\"$
\n" ); document.write( " $\"+R%2F4+=+-%28-14%29%5E2+-+28%2A%28-14%29++%2B+11040+\"$
\n" ); document.write( " $\"+R%2F4+=+11236+\"$
\n" ); document.write( "----------------
\n" ); document.write( "The manager should either increase the rent by
\n" ); document.write( " $\"+14%2A4+=+56+\"$ dollars, or he should decrease
\n" ); document.write( "the rent by $\"56\"$ dollars
\n" ); document.write( " $\"+368+%2B+56+=+424+\"$
\n" ); document.write( " $\"+368+-+56+=+312+\"$
\n" ); document.write( "either a rent of $424 or $312 will maximize revenue \n" ); document.write( "

\n" );