Question: The Iron Man Limited Partnership makes two products, paper and cardboard. The relationship between 7E, the film's annual profit (in thousands of dollars), and its output of each good is:

\(\pi \) = -50 + 40X + 30Y – 5X² – 4Y² – 3XY

where X is the firm's annual output of paper (in tons) and Y is the flint's annual output of cardboard (in tons).

a) find the output of each good that Iron Man LP should produce if it wants to maximize profit. (2 pts )

b) if the community in which the firm is located imposed a flat tax of $5,000 per year on the firm, will this alter the answer to part a? If so, how will the answer change? (1 pt.)