Chapter 10.2, Problem 37E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

** Advertising and sales—diminishing returns** Suppose that a company’s daily sales volume attributed to an advertising campaign is given by

(a) Find how long it will be before sales volume is maximized.

(b) Find how long it will be before the rate of change of sales volume is minimized. That is, find the point of diminishing returns.

**(a)**

To determine

**To calculate:** The number of days before sales is maximized where the sales function is

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,

**(b)**

To determine

**To calculate:** The number of days before rate of change of sales is minimized where the sales function is

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