Emily has a wood-working business and sells cornhole board sets. She determines a revenue function for selling x sets:
R(x) = 300x-0.5x2
And the total cost associated with producing these sets is given by:
C(x) = 4,000 + 50x

Q2.1 Find a function to represent the profit from producing and selling x sets of cornhole and simplify. Show your work.
Q2.2 Use this function to determine the number of sets of cornhole that should be sold in order to maximize profit and the maximum possible profit. Show work (whether algebraically or graphically) and answer with a complete sentence regarding how many sets Emily should sell and how much she would earn.
Q2.3 How many sets must Emily sell before she breaks even on her investment? Show work and answer with a complete sentence. (Hint: Emily doesn't sell incomplete sets).