Question 234888
I'll graph the Cost and Revenue
The graph will have number of hotdogs sold, {{{n}}} on the x-axis
Revenue, {{{r}}} and also cost, {{{c}}} are plotted on the y-axis
The cost of making {{{n}}} hotdogs is 
{{{c = .35n + .2n + 50}}}
{{{c = .55n + 50}}}
{{{r = 1*n}}}
Plotting these 2 lines on the same graph, the profit
is always {{{r - c}}}, which is the vertical distance
between the 2 lines
The break-even point is where the lines meet, or when {{{r = c}}}
{{{ graph( 400, 400, -20, 200, -20, 200, .55x + 50, x) }}}
At {{{r = c}}}, {{{n = .55n + 50}}}
{{{.45n = 50}}}
{{{n = 111}}}
Cost and Revenue are both $111 also