# A firm’s total profit equation is: p = -900 + 360x – x 2 – xy – y 2 + 250y Where x and y.

A firm’s total profit equation is: p = -900 + 360x – x 2 – xy – y 2 + 250y Where x and y represent the output levels for the two product lines (a) Use the substitution method to determine the profit-maximizing output levels of goods x and y subject to the side condition that the sum of the two product lines equal 500 units. (8 marks) (b) Use the Lagrange multiplier method to verify your answer to part a. (8 marks) (c) Calculate the firm’s total profits. (2 marks) (d) Calculate the Lagrange multiplier and comment on the meaning of the Lagrange multiplier. (4 marks) (e) Suppose that there were no combined output requirement. What are the profit maximizing levels of x and y? (6 marks) (f) Given your answer to part ‘e”, what is the firm’s total profits? (2 marks) [Total = 30 marks

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