14209an8.1-3

# 14209an8.1-3 - c Kendra Kilmer Section 8.1 Functions of...

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c Kendra Kilmer April 23, 2009 Section 8.1 - Functions of Several Variables Definition: An equation of the form z = f ( x , y ) describes a function of two independent variables if for each permissible ordered pair ( x , y ) , there is one and only one value of z determined by f ( x , y ) . Example 1: Given f ( x , y ) = 2 x 2 - 3 xy + y 2 - 4, find the following: a) f ( 3 , 0 ) b) f ( 1 , 2 ) c) f ( 4 , 1 ) Example 2: A company manufactures ten and three speed bicycles. The weekly demand and cost equations are p = 230 - 9 x + y , q = 130 + x - 4 y , C ( x , y ) = 200 + 80 x + 30 y where \$ p is the price of a ten speed bicycle, \$ q is the price of a three speed bicycle, x is the weekly demand for ten speed bicycles, y is the weekly demand for three speed bicycles, and C ( x , y ) is the cost function. a) Find the weekly revenue function and R ( 10 , 15 ) . b) Find the weekly profit function and P ( 10 , 15 ) 1

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c Kendra Kilmer April 23, 2009 Definition: The Cobb-Douglas production function is defined as f ( x , y ) = kx m y n where k , m , and n are positive constants with m + n = 1. Economists use this function to describe the number of units f ( x , y )
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