# QNewton - Gauss Siedel Solutions to the Production Surface...

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Gauss Siedel Solutions to the Production Surface Charles B. Moss September 2, 2011 1 wxMaxima Code to Parameterize the Pro- duction Surface Let’s start out by assuming a production function form f ( x 1 ,x 2 ,x 3 ) = 100 + 10 x 1 +15 x 2 +8 x 3 1 . 00 x 1 x 1 +0 . 10 x 1 x 2 0 . 04 x 1 x 3 0 . 70 x 2 x 2 +0 . 04 x 2 x 3 1 . 20 x 3 x 3 (1) Given this production function, we want to determine the points we want to generate three diFerent production points consistent with optimizing behav- ior. As a starting point, we will use the three diFerent sets of prices in Table 1. To set up the production function, derive the ±rst-order conditions, and then solve for the optimal points of production the wxMaxima code is /* Setup Basic Production Function */ f(x1,x2,x3):=100+10*x1+15*x2+8*x3-1.00*x1*x1+ 0.10*x1*x2-0.04*x1*x3-0.70*x2*x2+0.04*x2*x3-1.20*x3*x3; /* Derive First-Order Condtions */ c1(x1,x2,x3):=diff(f(x1,x2,x3),x1); c2(x1,x2,x3):=diff(f(x1,x2,x3),x2); 1

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Table 1: Input and Output Prices for Quadratic w 1 w 2 w 3 p 0.35 0.50 0.65 4.00 0.55 0.60 0.55 7.00 0.25 0.75 0.25 8.00 Table 2: Input and Output Levels x 1 x 2 x 3 y 5.4445 11.1099 3.3600 225.1927 5.4498 11.1393 3.3954 225.2005 5.4729 11.1358 3.4147 225.2025 c3(x1,x2,x3):=diff(f(x1,x2,x3),x3); /* Solve for the Optimal Point
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## This note was uploaded on 11/08/2011 for the course AEB 6184 taught by Professor Staff during the Spring '09 term at University of Florida.

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QNewton - Gauss Siedel Solutions to the Production Surface...

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