   Chapter 14.3, Problem 4E Mathematical Applications for the ...

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

Solutions

Chapter
Section Mathematical Applications for the ...

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

The total cost of producing an item is C ( x , y ) =   40   +   4 x   +   6 y + x 2 y 100 dollars where x is the cost per pound of raw materials and y is the cost per hour for labor. Find the function that can be used to determine how an increase of(a) $1 per pound of raw materials affects the total cost.(b)$1 per hour in labor costs affects the total cost.

(a)

To determine

To calculate: The function that can be used to determine how an increase of $1 per pound of raw materials affects the total cost. The total cost of producing an item is C(x,y)=40+4x+6y+x2y100 dollars, where x is the cost per pound of raw materials and y is the cost per hour of labor. Explanation Given Information: The total cost of producing an item is C(x,y)=40+4x+6y+x2y100 dollars, where x is the cost per pound of raw materials and y is the cost per hour of labor. Formula used: The rate of change of a function f(x,y) with respect to a variable x is given by the partial derivative of f with respect to x. For a function f(x,y), the partial derivative of f with respect to x is calculated by taking the derivative of f(x,y) with respect to x and keeping the other variable y constant. The partial derivative of f with respect to x is denoted by fx. Power of x rule for a real number n is such that, if f(x)=xn then f(x)=nxn1. Constant function rule for a constant c is such that, if f(x)=c then f(x)=0. The coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x) (b) To determine To calculate: The function that can be used to determine how an increase of$1 per hour in labor costs affects the total cost. The total cost of producing an item is C(x,y)=40+4x+6y+x2y100 dollars, where x is the cost per pound of raw materials and y is the cost per hour of labor.

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