Chapter 2.3, Problem 39E

To determine

To calculate:

The inequality equation and solution that represents the fraction of employees who work part time using the graphing utility

Answer to Problem 39E

The inequality equation and solution that represents the fraction of employees who work part time is $0\le x\le 24$ and $0\le f\le \frac{2}{3}$ respectively:

Explanation of Solution

Given information:

To total number of employees: $36$

The employee work for part time: $24$

Calculation:

Consider,

Number of employees work for part time: $x$

Know that:

  $0\le x\le 24$  .. . . . (1)

Know that:

The fraction of employees work for part time is:

  $\begin{array}{l}f=\frac{x}{36}\\ x=36f\end{array}$

Put $x=36f$ in eq. (1):

  $\begin{array}{l}0\le x\le 24\\ 0\le 36f\le 24\end{array}$

Multiply by $36$ on both sides of the above equations:

  $\begin{array}{l}0\le x\le 24\\ \frac{0}{36}\le \frac{36}{36}f\le \frac{24}{36}\\ 0\le f\le \frac{24}{36}\\ 0\le f\le \frac{2}{3}\end{array}$

So, the graph of the solution $0\le f\le \frac{2}{3}$ is: