The Paper Dragon Limited Partnership makes two products, paper and cardboard. The relationship between π, the firm’s annual profit (in thousands of dollars), and its output of each good is:
π = -50 + 40X + 30Y – 5X^2 – 4Y^2 – 3XY
where X is the firm’s annual output of paper (in tons) and Y is the firm’s annual output of cardboard (in tons).
a. find the output of each good that Paper Dragon LP should produce if it wants to maximize profit.
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?