11Breview2

11Breview2 - critical values in this problem a H u,v,w = 2...

This preview shows pages 1–2. Sign up to view the full content.

econ 11b ucsc ams 11b Review Questions 2 Optimization in several variables, I 1. Find the quadratic Taylor polynomial for the function f ( x,y ) = p 5 x + 2 y centered at the point ( x 0 ,y 0 ) = (10 , 7). 2. 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. 3. 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 . Find the prices that ACME should charge to maximize their proﬁt. Justify your claim that the prices you found yield the absolute maximum proﬁt. 4. Find the critical point(s) of the functions below. You do not need to classify the

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 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 . 5. A ﬁrm sells two competing products, A and B. The joint demand equations for these products are Q A = 80-3 2 P A + 2 P B and Q B = 60 + 2 P A-3 P B , where Q A and Q B are the weekly demand for products A and B, respectively, and P A and P B are the prices of these products. Find the prices that the ﬁrm should charge to maximize the ﬁrm’s revenue , the quantities that the ﬁrm sells at these prices and the (maximum) revenue the ﬁrm generates. Justify your claim that the prices you found yield the maximum revenue....
View Full Document

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

Page1 / 2

11Breview2 - critical values in this problem a H u,v,w = 2...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online