   Chapter 10.4, Problem 8E ### 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

# Production costs Suppose that the monthly cost in dollars of mining a certain ore is related to the number of pieces of equipment used according to C = 25 , 000 x + 870 , 000 x ,   x > 0 where x is the number of pieces of equipment used. Using how many pieces of equipment will minimize the cost?

To determine

To calculate: The number of pieces to minimize the cost.

Explanation

Given Information:

The equation for cost is given as

C=25,000x+870,000x, x>0

Where x is the number of pieces used.

Formula used:

To find the minimum value, calculate the relevant stationary value of an equation. Differentiate the function with respect to the independent variable and equate it to 0. the relevant value is the stationary value that satisfies the provided conditions.

The power rule is used for a function in which the expression can be written as every term raised to a power (be it fractional, positive or negative). For the function f(x)=xn, the derivative is

ddx[xn]=nxn1

Calculation:

The equation for cost is given as:

C=25,000x+870,000x, x>0

Where x is the number of pieces used.

To find the stationary value for C=25,000x+870,000x, differentiate the equation with respect to the independent variable x to get

C'=25,000870,000x2

Put C'=0 to get x,

25,000870,000x2=025,000=870,000x2x=±870,00025,000x=±5

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