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.
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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Question
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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