Question 440190
Let {{{k}}} = the number of {{{50}}} cent increases in price
Let {{{R}}} = revenue
given:
{{{ R =  (42000 - 5000k)*(250 + 50k) }}} (in cents)
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{{{ R =  (42000 - 5000k)*(250 + 50k) }}}
{{{ R = 10500000 - 1250000k + 2100000k - 250000k^2 }}}
{{{ R = -25k^2 + 85k + 1050 }}}
{{{ R = -5k^2 + 17k + 210 }}}
This is a parabola with a maximum, since the
coefficient of {{{k^2}}} is minus.
The max is at {{{ -b/(2a) }}} where
{{{a = -5}}}
{{{b = 17}}}
{{{ -b/(2a) = -17/(-10) = 1.7
Since {{{k}}} is  the number of {{{50}}} cent increases in price,
{{{ 50*1.7 = 85 }}} cents is the increase over $2.50 that
Steve should allow
{{{ 2.5 + .85 = 3.35 }}}
He should charge $3.35 per hot dog
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You can check this by putting {{{334}}}, {{{335}}} and 
{{{336}}} into 
{{{ R =  (42000 - 5000k)*(250 + 50k) }}}
and seeing ir {{{R}}} peaks at {{{335}}}