11Breview2

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: . Find the prices that ACME should charge to maximize their prot. Justify your claim that the prices you found yield the absolute maximum prot. 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 ....
View Full Document

Ask a homework question - tutors are online