Chapter 4.3, Problem 66PPS

To determine

To calculate: The price range of the web sites that will be profitable for the company.

Answer to Problem 66PPS

The price range that will be profitable for the company is $\text{9}\text{.25 to 13}\text{.75}$ .

Explanation of Solution

Given information:

A company determined that their profitability of the product is determined by the model $\text{P}\left(x\right)=-16x^2+368x-2035$ , where x is the price of each web site and $\text{P}\left(x\right)$ is company’s profit.

Formula used:

Solution of a polynomial equation is calculated using middle term splitting method and then common factors are taken out and simplified.

Calculation:

Consider the given information that “A company determined that their profitability of the product is determined by the model $\text{P}\left(x\right)=-16x^2+368x-2035$ , where x is the price of each web site and $\text{P}\left(x\right)$ is company’s profit.”

The range will be the solution set of the model that determines company’s profitability. The company will be profitable between the range that makes the polynomial zero.

Recall that solution of a polynomial equation is calculated using middle term splitting method and then common factors are taken out and simplified.

Apply it,

Factorize $16x^2-368x+2035$ to find the range,

  $\begin{array}{c}16x^2-368x+2035=16x^2-220x-148x+2035\\ =4x\left(4x-55\right)-37\left(4x-55\right)\\ =\left(4x-37\right)\left(4x-55\right)\end{array}$

Therefore, either $\begin{array}{c}4x-37=0\text{ or }4x-55=0\\ x=9.25\text{ or }x=13.75\end{array}$ .

Thus, price range that will be profitable for the company is $\text{9}\text{.25 to 13}\text{.75}$ .