Question 590084
Let {{{ g }}} = gallons of gas sold per hour
Let {{{ p }}} = price per gallon in dollars
Plot {{{ g }}} on the vertical axis
Plot {{{ p }}} on the horizontal
use the point slope formula
{{{ ( g - 800 ) / ( p - 2.4 ) = ( 900 - 800 ) / ( 2.15 - 2.4 ) }}}
{{{ ( g - 800 ) / ( p - 2.4 ) = 100 / (-.25) }}}
{{{ ( g - 800 ) / ( p - 2.4 ) = -400 }}}
{{{ g - 800 = -400*( p - 2.4 ) }}}
{{{ g - 800 = -400p + 960 }}}
{{{ g = -400p + 1760 }}}
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(a)
{{{ g = -400*2.35 + 1760 }}}
{{{ g = -940 + 1760 }}}
{{{ g = 820 }}}
820 gallons/hr would be sold
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(b)
{{{ g = -400p + 1760 }}}
{{{ 1600 = -400p + 1760 }}}
{{{ 400p = 1760 - 1600 }}}
{{{ 400p = 160 }}}
{{{ p = .4 }}}
The price must be $ .40 / gallon to sell 1600 gallons/hr
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(c)
(1) {{{ 2.15*900 = 1935 }}}
Revenue = $ 1,935
(2)  {{{ 2.4*800 = 1920 }}}
Revenue = $ 1,920
(3) {{{ 2.35*820 = 1927 }}}
Revenue = $ 1,927
{{{ .4*1600 = 640 }}}
Revenue = $640
$2.15 / gallon gives the most revenue