psNPP1Qu - Fall 2007 Problem Set #11 First NPP Problem Set...

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ARE211 Problem Set #11 First NPP Problem Set Due date: Nov 27 (1) Consider the following maximization problem (solve it graphically): max x 1 ,x 2 f ( x 1 , x 2 ) with f ( x 1 , x 2 ) = - x 1 subject to g 1 : - x 3 1 + x 2 0 and g 2 : - x 3 1 - x 2 0. a) What is the solution to the maximization problem? b) Is the Mantra satisFed for the solution to part a). If yes, write the gradient of the objective function as a postive linear combination of the gradients of the contstraints that are satisFed with equality. If not, explain why? c) Now, slightly change the problem and let the second constraint be g 2 : - x 3 1 - ex 1 - x 2 0 for e > 0 Again, what is the solution to your problem? d) ±or the revised problem in part c), is the Mantra satisFed. If yes, write the gradi- ent of the objective function as a postive linear combination of the gradients of the contstraints that are satisFed with equality. If not, explain why? (2) Consider the following minimization problem
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psNPP1Qu - Fall 2007 Problem Set #11 First NPP Problem Set...

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