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Maximizing Profit on Paper and Cardboard Production

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A limited partnership makes two products, paper and cardboard. The relationship between the firm's annual profit (in thousands of dollars), and its output of each good is:

C(x,y)  = -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).

*Find the output of each good that the LP should produce if it wants to maximize profit.

*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? If so, how will the answer change?

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Solution Summary

The expert examines maximizing profits on paper and cardboard production/

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define the profit function

C(x,y) = -50 + 40X + 30Y - 5X^2 - 4Y^2 - 3XY

to find the max, we need to find critial points (points where gradient = 0)

dP/dX ...

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