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(X, Y) = -900 + 360X - X2 - XY - Y2 + 250Y
Where X and Y represent the output levels for the two product lines.
(a) Using Lagrange multiplier method, determine the profit-maximizing output levels of goods X and Y given that the sum of the two product lines equal 500 units.
[10 marks]
(b) Calculate the firm's total profits.
[2 marks]
(c) What is the interpretation of the Lagrange multiplier?



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