3. (i) Write down the Lagrange function for the following optimization problem. Optimize x - y +2z subject to constraints x² + y² +z² = 1 and x+y+ z = 0. (ii) Use the technique of Lagrange multipliers to find the values of x and y which optimize the function U (x,y) = x - 3y - xy subject to the constraint x+y = 6. (iii) Estimate the U (x,y) at the values of x and y derived in above (ii).

3. (i) Write down the Lagrange function for the following optimization problem. Optimize x - y +2z subject to constraints x² + y² +z² = 1 and x+y+ z = 0. (ii) Use the technique of Lagrange multipliers to find the values of x and y which optimize the function U (x,y) = x - 3y - xy subject to the constraint x+y = 6. (iii) Estimate the U (x,y) at the values of x and y derived in above (ii).

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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