Chapter 14.3, Problem 2E

### 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 manufacture of 1 unit of a product has a cost (in dollars) given by C ( x , y ,   z )   = 10   +   8 x   + 3 y + 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 $16 per pound, the cost of the second raw material is$8 per pound, and labor costs $18 per work-hour, what will it cost to produce 1 unit of the product?(b) Find and interpret the partial derivative of C with respect to x. (a) To determine To calculate: The cost to produce 1 unit of the product if the cost of the first raw material is$16 per pound, the cost of the second raw material is $8 per pound, and labor costs$18 per hour. The manufacture of 1 unit of a product has a cost (in dollars) given by C(x,y,z)=10+8x+3y+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.

Explanation

Given Information:

The manufacture of 1 unit of a product has a cost (in dollars) given by C(x,y,z)=10+8x+3y+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. Also, the cost of the first raw material is $16 per pound, the cost of the second raw material is$8 per pound, and labor costs $18 per hour. Calculation: Consider the problem, the manufacture of 1 unit of a product has a cost (in dollars) given by C(x,y,z)=10+8x+3y+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. The provided function is C(x,y,z)=10+8x+3y+z. Also, the cost of the first raw material is$16 per pound, the cost of the second raw material is $8 per pound, and labor costs$18 per hour.

Thus, x=16,y=8,z=18

(b)

To determine

To calculate: The partial derivative of C with respect to x. The manufacture of 1 unit of a product has a cost (in dollars) given by C(x,y,z)=10+8x+3y+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. Interpret the answer.

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