lagrange2-nokey - ECON 331 Study Questions for Chapter 12:...

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ECON 331 Study Questions for Chapter 12: Lagrange Multiplier Method Kevin Wainwright SHORT ANSWER. Show all your work. In each case, check 2nd order conditions 1) Use the method of Lagrange multipliers to find the critical points of f ( x , y , z ) = 2 x + 4 y - 4 z subject to the constraint x 2 + y 2 + z 2 = 9. 1) 2) Use the method of Lagrange multipliers to determine the critical points of f ( x , y , z ) = x 2 - 3 y 2 - z 2 + 6 subject to the constraint 5 x - 3 y + z = 21. 2) 3) The Cobb-Douglas production function for a company is given by P ( k , l ) = 163 k 1/5 l 4/5 where P is the monthly production value when k is the number of units of capital and l is the number of units of labor. Suppose that capital costs $105 per unit, labor costs $70 per unit, and the total cost of capital and labor is limited to $152,250. Use Lagrange Multiplier's to write the system of equations you would use to find the number of units of capital and labor that maximize production. 3)
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This note was uploaded on 09/13/2009 for the course EOCNOMICS Econ 331 taught by Professor Kelvinkwainger during the Spring '09 term at Simon Fraser.

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lagrange2-nokey - ECON 331 Study Questions for Chapter 12:...

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