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Mathematical Applications for the ...

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

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BuyFindarrow_forward

Mathematical Applications for the ...

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

Output The following figure shows a typical graph of output y (in thousands of dollars) as a function of capital investment I (also in thousands of dollars).

(a) Is the point of diminishing returns closest to the point at which 1   =   20 ,   1 60 ,  or  I =   120 ? Explain.

(b) The average output per dollar of capital investment is defined as the total output divided by the amount of capital investment; that is,

Average output = f ( I ) I

Calculate the slope of a line from (0, 0) to an arbitrary point ( I , f ( I ) ) on the output graph. How is this slope related to the average output?

(c) Is the maximum average output attained when the capital investment is closest to I =   40 ,  to  I =   70 ,  or to  I =   140 ? Explain.

Chapter 10, Problem 39RE, 39. Output The following figure shows a typical graph of output y (in thousands of dollars) as a

(a)

To determine

The capital investment at which the point of diminishing returns to closest among I=20, I=60, and I=120 with reason for the graph,

Mathematical Applications for the Management, Life, and Social Sciences, Chapter 10, Problem 39RE , additional homework tip  1

Explanation

Given Information:

The provided graph of the capital investment and the output is shown below:

Explanation:

The critical values are the only values at which the graph can have turning points, the derivative cannot change sign anywhere except at the critical value.

This, in an interval between two critical values, the sign of the derivative at any value in the interval will be the sign of the derivative at all values in the interval.

If the first derivative of f is 0 at x0 but does not change from positive to negative or from negative to positive as x passes through x0, then the critical point at x0 is neither a relative maximum nor a relative minimum

(b)

To determine

To calculate: The slope of a line from (0,0) to an arbitrary point (I,f(I)) on the output and how the slope related to the average output if the figure shows a typical graph of output y (in thousands of dollars) as a function of capital investment I where the average output is, Average output=f(I)I.

Mathematical Applications for the Management, Life, and Social Sciences, Chapter 10, Problem 39RE , additional homework tip  2.

(c)

To determine

The maximum average point attained at I=40,I=70 or I=140, when the capital investment is closest, if the figure shows a typical graph of output y (in thousands of dollars) as a function of capital investment I.

Mathematical Applications for the Management, Life, and Social Sciences, Chapter 10, Problem 39RE , additional homework tip  3

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Chapter 10 Solutions

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