Chapter 9.3, Problem 47E

Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

Labor force and output The monthly output at the Olek Carpet Mill is Q ( x ) = 15 , 000 + 2 x 2  units,  ( 40 ≤ x ≤ 60 ) where x is the number of workers employed at the mill. If there are currently 50 workers, find the instantaneous rate of change of monthly output with respect to the number of workers. That is, find Q'(50).

To determine

To calculate: The instantaneous rate of change of monthly output with respect to number of workers if total workers are 50. The monthly output is given as

Q(x)=15,000+2x2,,

Where x is the number of workers employed and 40x60.

Also find Q(50).

Explanation

Given Information:

Total number of workers are 50. The monthly output is given as

Q(x)=15,000+2x2,,

Where x is the number of workers employed and 40â‰¤xâ‰¤60.

Formula used:

If a function f(x) is defined in the interval [x,x+h] then instantaneous rate of change is given by the derivative of the function as,

fâ€²(x)=limhâ†’0f(x+h)âˆ’f(x)(x+h)âˆ’x

Calculation:

Consider the provided statements,

Total number of workers are 50. The monthly output is given as,

Q(x)=15,000+2x2

Where x is the number of workers employed and 40â‰¤xâ‰¤60.

Substitute x=x+h in Q(x) to get,

Q(x+h)=15,000+2(x+h)2=15,000+2(

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