Chapter 14.3, Problem 1E

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# The cost (in dollars) of manufacturing one item is given by C ( x , y ) =   30   + 3 x + 5 y where x is the cost of 1 hour of labor and y is the cost of1 pound of material.(a) If the hourly cost of labor is $20 and the material costs$3 per pound, what is the cost of manufacturing one of these items?(b) Find and interpret the partial derivative of C with respect to x.

(a)

To determine

To calculate: The cost of manufacturing one of the items if the hourly cost of labor is $20 and the material costs$3 per round. The cost (in dollars) of manufacturing one item is given by C(x,y)=30+3x+5y where x is the cost of 1 hour of labor and y is the cost of 1 pound of material.

Explanation

Given Information:

The cost (in dollars) of manufacturing one item is given by C(x,y)=30+3x+5y where x is the cost of 1 hour of labor and y is the cost of 1 pound of material. Also, the hourly cost of labor is $20 and the material costs$3 per round.

Calculation:

Consider the problem,

The cost (in dollars) of manufacturing one item is given by C(x,y)=30+3x+5y where x is the cost of 1 hour of labor and y is the cost of 1 pound of material.

The provided function is C(x,y)=30+3x+5y.

Also, the hourly cost of labor is $20 and the material costs$3 per round.

Thus, x=20,y=3

(b)

To determine

To calculate: The partial derivative of C with respect to x. The cost (in dollars) of manufacturing one item is given by C(x,y)=30+3x+5y where x is the cost of 1 hour of labor and y is the cost of 1 pound of material. Interpret the answer.

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