AEB 3510 partial derivaties applications solutions0

AEB 3510 partial derivaties applications solutions0 - AEB...

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AEB 3510 PROBLEM SET 3: APPLICATIONS OF PARTIAL DERIVATIVES 1. Solution: (a) The marginal productivity of labor is given by: ( , ) 40 3 f x y x y x (b) The marginal productivity of capital is given by: ( , ) 3 f x y x y (c) When x=250 and y=100, the marginal productivity of land and capital is: ( 250, 100) 40(250) 3(100) 10300 f x y x ( 250, 100) 3(250) 750 f x y y The marginal product of labor is 10,300 and the marginal product of capital is 750 when the amount of labor and capital used are 250 and 100 units, respectively. 2. Solution: (a) The marginal profit associated with an additional unit (thousand dollars) of inventory is given by: 3 y x (b) The marginal profit associated with an additional unit (thousand square feet) of floor space is given by: 25 x y
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3. Solution: (a) The marginal revenue generated from the sale of an additional TV is given by: 2 R x y x (b) The marginal revenue generated from the sale of an additional computer is given by: 2 R x y y (c) When x=50 and y=100, the marginal revenue from the sale of an additional TV is: ( 50, 100) 2(50) 100 200 R x y x 4. Solution: (a)
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