Answer
a) $R(2)=4000$ dollars
$R(4)=4000$ dollars
These values represent profit when setting the bars at \$$2$ and \$$4$, respectively.
b) There will always be a positive revenue, but there is not a constant proportion between the price of a chocolate bar and the total revenue.
c) The maximum revenue is \$$4500$ when pricing the chocolate bar at \$$3$ per bar.
Work Step by Step
a) $R(2)=-500(2)^2+3000\cdot2=$
$-500\cdot4+6000=$
$-2000+6000=4000$ dollars
$R(4)=-500(4)^2+3000\cdot4=$
$-500\cdot16+12000=$
$-8000+12000=4000$ dollars
b) One can see when graphing the equation that as the price of the chocolate increases from zero, the revenue increases as well until the price of a chocolate bar is \$$3$. When pricing above that, the revenue starts to decline.
c) The maximum revenue is represented by the top of the crest that forms in the function.