11Breview3

# 11Breview3 - econ 11b ucsc ams 11b Review Questions 3...

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econ 11b ucsc ams 11b Review Questions 3 Optimization in several variables, II 1. Find the optimal values for the constrained optimization problems below. You may assume that (one of) the critical point(s) you ﬁnd yield(s) the desired optimum. a. Find the minimum value of f ( x,y ) = x 2 + y 2 subject to 3 x + 5 y = 68. b. Find the maximum value of g ( x,y,z ) = 20 x 1 / 2 y 1 / 3 z 1 / 6 , subject to the constraint 5 x + 4 y + 7 z = 1680. c. Find the maximum and minimum values of the function h ( x,y ) = 3 x + 5 y subject to the constraint x 2 + y 2 = 136. 2. Jack’s (gustatory) utility function is U ( x,y,z ) = 5 ln x + 7 ln y + 18 ln z , where x is the number of fast-food meals Jack consumes in a month; y is the number of ‘diner’ meals he consumes in a month; and z is the number of ‘fancy restaurant’ meals he consumes in a month. The average price of a fast-food meal is p x = \$4 . 00; the average price of a ‘diner’ meal is p y = \$8 . 00; and the average price of a ‘fancy restaurant’ meal is

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## This note was uploaded on 09/16/2011 for the course ECON 11B taught by Professor Binici during the Spring '08 term at UCSC.

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11Breview3 - econ 11b ucsc ams 11b Review Questions 3...

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