11Breview2

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

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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
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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 rm 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 rm should charge to maximize the rms revenue , the quantities that the rm sells at these prices and the (maximum) revenue the rm generates. Justify your claim that the prices you found yield the maximum revenue....
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11Breview2 - critical values in this problem. a. H ( u,v,w...

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