Chapter 6.6, Problem 36PPS

a.

To determine

To find: Variables and System of inequalities of given situation.

Answer to Problem 36PPS

Variables are

‘ $n$ ’ be number of notebooks.

‘ $p$ ’ be number of pens

Inequalities are

  $\begin{array}{l}n\ge 20\\ p\ge 50\\ 2.50n+1.25p\ge 150\end{array}$

Explanation of Solution

Given information:

They would like to sell at least 20 notebooks and 50 pens per week.

Goal of earning is at least $150 per week.

Cost of each notebook = $2.50

Cost of each pen = $1.25

Let ‘ $n$ ’ be number of notebooks.

Let ‘ $p$ ’ be number of pens.

From given information

They would like to sell at least 20 notebooks and 50 pens per week.

We get

  $n\ge 20$ -----------(1)

  $p\ge 50$ --------(2)

Goal of earning is at least $150 per week

Cost of ‘ $n$ ‘ notebooks + Cost of ‘ $p$ ’ pens $\ge$ 150

  $\Rightarrow 2.50n+1.25p\ge 150$ -----------(3)

Equation-(1) and Equation-(2) and Equation-(3) represents system of inequalities of given situation.

b.

To determine

To find: Graph of this system.

Explanation of Solution

Given information:

They would like to sell at least 20 notebooks and 50 pens per week.

Goal of earning is at least $150 per week.

Cost of each notebook = $2.50

Cost of each pen = $1.25

Inequalities are

  $\begin{array}{l}n\ge 20\\ p\ge 50\\ 2.50n+1.25p\ge 150\end{array}$

Graph of given inequalities is

Here

Red colour represents $n\ge 20$ .

Blue colour represents $p\ge 50$ .

Green colour represents $2.50n+1.25p\ge 150$ .

Common region of Red colour, Blue colour and Green colour is the solution of above inequalities.

c.

To determine

To find: One possible solution.

Answer to Problem 36PPS

  $\left(50,80\right)$

Number of Notebooks =50

Number of Pens = 80

Explanation of Solution

Given information:

They would like to sell at least 20 notebooks and 50 pens per week.

Goal of earning is at least $150 per week.

Cost of each notebook = $2.50

Cost of each pen = $1.25

Red colour represents $n\ge 20$ .

Blue colour represents $p\ge 50$ .

Green colour represents $2.50n+1.25p\ge 150$ .

Common region of Red colour, Blue colour and Green colour is the solution of above inequalities.

As $\left(50,80\right)$ is in the common region of Blue, Red and Green colour.

So $\left(50,80\right)$ is the one possible solution.