Question 1051678
Let {{{ n }}} = number of $.50 increases in price
Let {{{ P }}} = the price of {{{ 60 + 10n }}} hot dogs
{{{ P = ( 60 + 10n )*( 4 - .5n ) }}}
{{{ P = 240 + 40n - 30n - 5n^2 }}}
{{{ P = -5n^2 + 10n + 240 }}}
The n-value of {{{ P }}} is 
{{{ n[max] =  -b/(2a) }}}
{{{ n[max] = -10/(2*(-5)) }}}
{{{ n[max] = 1 }}}
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{{{ n = 1 }}}
{{{ P = ( 60 + 10*1 )*( 4 - .5*1 ) }}}
{{{ P = 70*3.5 }}}
{{{ P = 245 }}}
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(a)
The food truck should charge $3.50 per hot dog
(b)
The maximum daily revenue is $245
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check:
Here's the plot:
{{{ graph( 400, 400, -1, 10, -30, 280, -5x^2 + 10x + 240 ) }}}