C(x, y, z) = 90 + 6x + 4y + z where x is the cost of 1 pound of one raw material, y is the cost of 1 pound of a second raw material, and z is the cost of 1 work-hour of labor. (a) If the cost of the first raw material is $11 per pound, the cost of the second raw material is $8 per pound, and labor costs $17 per work-hour, what will it cost to produce 1 unit of the product (in dollars)? $ (b) Find the partial derivative of C with respect to x. Cx =     Interpret the partial derivative of C with respect to x. The cost (in dollars) to manufacture 1 unit of a product will increase by $4 for a $1 increase in y and z if x is held constant.The cost (in dollars) to manufacture 1 unit of a product will increase by $90 for a $1 increase in x if y and z are held constant.     The cost (in dollars) to manufacture 1 unit of a product will increase by $4 for a $1 increase in x if y and z are held constant.The cost (in dollars) to manufacture 1 unit of a product will increase by $6 for a $1 increase in x if y and z are held constant.The cost (in dollars) to manufacture 1 unit of a product will increase by $6 for a $1 increase in y and z if x is held constant.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 17EQ
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The manufacture of 1 unit of a product has a cost (in dollars) given by
C(x, y, z) = 90 + 6x + 4y + z
where x is the cost of 1 pound of one raw material, y is the cost of 1 pound of a second raw material, and z is the cost of 1 work-hour of labor.
(a)
If the cost of the first raw material is $11 per pound, the cost of the second raw material is $8 per pound, and labor costs $17 per work-hour, what will it cost to produce 1 unit of the product (in dollars)?
$
(b)
Find the partial derivative of C with respect to x.
Cx =
 
 
Interpret the partial derivative of C with respect to x.
The cost (in dollars) to manufacture 1 unit of a product will increase by $4 for a $1 increase in y and z if x is held constant.The cost (in dollars) to manufacture 1 unit of a product will increase by $90 for a $1 increase in x if y and z are held constant.     The cost (in dollars) to manufacture 1 unit of a product will increase by $4 for a $1 increase in x if y and z are held constant.The cost (in dollars) to manufacture 1 unit of a product will increase by $6 for a $1 increase in x if y and z are held constant.The cost (in dollars) to manufacture 1 unit of a product will increase by $6 for a $1 increase in y and z if x is held constant.
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