we have to maximize profit....

so, we have to maximize funtion f(x)=px-x = (5x-xln(x)-x)

to optimize we equate the derivative to zero, hence: f'(x) = 5 - x/x - ln(x) -1 = 0

solving we get ln(x) = 3, so x = e3

put this value in p = 5 - ln(x) = 5 - ln(e3) = 2

so price should be $2

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