Chapter 10.2, Problem 35E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

** Production** Suppose that the total number of units produced by a worker in

(a) Find the number of hours before production is maximized.

(b) Find the number of hours before the rate of production is maximized. That is, find the point of diminishing returns.

**(a)**

To determine

**To calculate:** The number of hours before production is maximized where the production function is *t* hours of an 8 hours shift.

Explanation

**Given Information:**

The provided function is

**Formula used:**

To find relative maxima and minima of a function,

1. Set the first derivative of the function to zero,

2. Substitute the critical values into

3. Calculate the sign of the function to the left and right of the critical values.

(a) If

(b) If

**Calculation:**

Consider the function

Calculate the first derivative of the function

Set the first derivative equal to 0.

Thus, either

First consider

Solve for *t*.

Now consider

Solve for *t*.

Thus, the critical points are

**(b)**

To determine

**To calculate:** The number of hours before rate of production is maximized where the production function is *t* hours of an 8 hours shift.

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