Chapter 3.2, Problem 17PPS

To determine

To plot: The graph for the number of hours to work at each job if Rondell wants to make the trip.

Explanation of Solution

Giveninformation:

Earning at pizza palace per hour is $\text{\$}9$

Earning at car wash per hour is $\text{\$}12$

The amount to save = $\text{\$}925$

Calculation :

Let $x$ is the cost to earn an hour working at the Pizza Palace.

Let $y$ is the cost to earn an hour working at a car wash

By law, cannot work more than 25 hours per week and 8 weeks for Latin class.

It means,

  $25\times 8=200$ hours

The inequality is as follows,

  $x+y\le 200$

Now $\text{\$}9$ earn at pizza palace and $\text{\$}12$ earn at a car wash and total save at least $\text{\$}925$

The inequality is as follows,

  $9x+12y\ge 925$

Consider the following system of inequalities:

  $\begin{array}{l}x+y\le 200\dots (1)\\ 9x+12y\ge 925\dots \dots (2)\end{array}$

Use maple to plot the graph of the above equation,

  

To test the solution by substituting (0, 0) for $x$ and $y$ in each equation,

First, substitute the points $(x,y)=(0,0)$ in equation (1) and simplify it as follows,

  $\begin{array}{l}x+y\le 200\\ 0+0\le 200\\ 0\le 200\end{array}$

This is true, means 0 is less than 200.

Now, substitute the points $(x,y)=(0,0)$ in equation (2) and $simplify$ it as follows,

  $\begin{array}{l}9x+12y\ge 925\\ 9(0)+12(0)\ge 925\\ 0\ge 925\end{array}$

This is false, means 0 is not greater than 925.

Hence, the graph of the inequalities overlap, equation (1) goes towards origin and equation (2) goes far away from origin. The solution is in the shaded green region.