11Breview2

# 11Breview2 - Find the prices that ACME should charge to...

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ucsc econ/ams 11b Review Questions 2 Optimization in several variables, I 1. Find the critical points of the functions below, and classify their critical values (as relative minimum, relative maximum, or neither) using the second derivative test. a. f ( x,y ) = 3 x 2 - 12 xy + 19 y 2 - 2 x - 4 y + 5. b. g ( s,t ) = s 3 + 3 t 2 + 12 st + 2. c. h ( u,v ) = u 3 + v 3 - 3 u 2 - 3 v + 5. 2. ACME Widgets produces two competing products, type A widgets and type B widgets. The joint demand functions for these products are Q A = 100 - 3 P A + 2 P B and Q B = 60 + 2 P A - 2 P B and ACME’s cost function is C = 20 Q A + 30 Q B + 1200
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Unformatted text preview: . Find the prices that ACME should charge to maximize their proﬁt. Justify your claim that the prices you found yield the absolute maximum proﬁt. 3. Find the critical point(s) of the functions below. You do not need to classify the critical values in this problem. a. H ( u,v,w ) = 2 u 2 + v 2-3 w 2 + 2 uv + 4 uw-2 vw . b. F ( x,y,z ) = 30 x 1 / 3 y 2 / 3-z (5 x + 8 y-400). c. G ( w,x,y,z ) = x 2 + 2 y 2 + 4 z 2-2 wx-5 wy-3 wz + 300 w ....
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## This note was uploaded on 03/16/2010 for the course ECON 1xx taught by Professor Gp during the Spring '10 term at UCSC.

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