Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.8 - Modeling Using Variation - Exercise Set - Page 426: 57

Answer

If the price of the product is either kept constant or reduced, then the advertisement expenditure can be increased.

Work Step by Step

Let the product be a shaving cream, denoted by S. According to the conditions given, ${{S}_{d}}=k\frac{A}{P}$ where ${{S}_{d}}=$ Demand of the shaving cream $k=$ Constant $A=$ Advertising expenditure $P=$ Price of the product Let the demand of the product be $1000$ units, the advertisement expenditure be around $\$100,000,$ and the price of the product be $\$200$. Substitute the values in the formula stated above: $\begin{align} & {{S}_{d}}=k\frac{A}{P} \\ & 1000=k\frac{100,000}{200} \\ & k=2 \end{align}$ Now, if the advertising expenditure is increased to $\$200,000$ and the price is kept constant, we get $\begin{align} & {{S}_{d}}=k\frac{A}{P} \\ & {{S}_{d}}=2\times \frac{200,000}{200} \\ & {{S}_{d}}=2000 \end{align}$ So, the demand for the product increases on increasing the advertising expenditure, along with keeping the price constant or reducing the price of the product. There are other factors as well that affect the demand of the product such as marketing schemes and weather conditions, and they can be included as well. Thus, if the price of the product is either kept constant or reduced, then the advertisement expenditure can be increased.
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