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A firm produces two goods: widgets (X) and woozles (Y). Its profit function is given by: P= 55X - 2X 2 - XY - 3Y

A firm produces two goods: widgets (X) and woozles (Y). Its profit function is given by:

P= 55X - 2X²- XY - 3Y²+ 100Y

and its maximum output capacity is X + Y = 17.

(a)Use the Lagrangian method to calculate the output mix the firm should produce.

(b)Estimate the effects on profits if output capacity is expanded by 1 unit.

(c)You are hired by the firm to evaluate a proposal from its Engineering Department that the firm's output capacity be expanded to 33. Do you agree with the proposal? If not, what output capacity would you recommend?

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