Question 534954
Let {{{n}}} = number of $4 in rent ( up or down )
Let {{{ R }}} = manager's revenue
For increase in rent:
{{{ R = ( 120 - n )*( 368 + 4n ) }}}
{{{ R = 44160 - 368n + 480n - 4n^2 }}}
{{{ R = -4n^2 + 112n + 44160 }}}
{{{ R/4 = -n^2 + 28n  + 11040 }}}
and, for decrease in rent:
{{{ R = ( 120 + n )*( 368 - 4n ) }}}
{{{ R = 44160 + 368n - 480n - 4n^2 }}}
{{{ R = -4n^2 -112n + 44160 }}}
{{{ R/4 = -n^2 - 28n + 11040 }}}
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For rent increase,
{{{ n[max] = -(28/(-2)) }}}
{{{ n[max] = 14 }}}
{{{ R/4 = -14^2 + 28*14  + 11040 }}}
{{{ R/4 = -196 + 392 + 11040 }}}
{{{ R/4 = 11236 }}}
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For rent decrease,
{{{ n[max] = -(-28)/(-2)) }}}
{{{ n[max] = -14 }}}
{{{ R/4 = -(-14)^2 - 28*(-14)  + 11040 }}}
{{{ R/4 = 11236 }}}
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The manager should either increase the rent by
{{{ 14*4 = 56 }}} dollars, or he should decrease
the rent by {{{56}}} dollars
{{{ 368 + 56 = 424 }}}
{{{ 368 - 56 = 312 }}}
either a rent of $424 or $312 will maximize revenue