Q. 31 - Precalculus Enhanced with Graphing Utilities

Question

Refer to Example 1 on page 159. Notice that if the price charged for the calculators is $\backslash (0$ or $\backslash )140$ the revenue is$\backslash (0.$ It is easy to explain why revenue would be $\backslash )0$if the price charged is $\backslash (0,$ but how can revenue be$\backslash )0$ if the price charged is $\$140?$

Step-by-Step Solution

Answer

The reason why there is no revenue is that when prices are very high the demand for a certain item is almost zero. Since no one would like to buy an item for a very expensive price. Meanwhile, when the prices are reasonable many people would like to buy the product which would mean that the demand would be high.

Step 1. Introduction

Notice that if the price for the calculator is $\$0 or \$140$ the revenue is $\$0.$ We need to explain why the revenue would be $\$0$ if the price charge is $\$0$ and now can revenue be $\$0$if the price charged is $\$140.$

Step 2. Explanation

We know that the demand equation is,

$x=21000-150p.$

Where $p$ is the price of calculator. We can derive the equation as,

$R=x{p}^2,$where $x$ is the demand equation.

When the price of the calculator is $\$140$ the demand will become $0.$ Hence when solving for the revenue at a price of $\$140.$ We know that $x=0,$therefore the revenue will also be $0.$