Chapter 6.8, Problem 25PPS

(a)

To determine

To define: The variables and to write a system of inequalities

Answer to Problem 25PPS

The inequalities are $10,000\le y\le 150,000$ and $1000\le x\le 17000$

Explanation of Solution

Given:

Ice resurfaces, rinks of at least $1000$ square feet and up to $17000$ square feet Price ranges from $10,000$ to $150,000$ square feet

Calculation:

Let $x$ represents the square footage of the rink

Let $y$ represents the price of the resurfacing

Now the inequalities will be $10,000\le y\le 150,000$ and $1000\le x\le 17000$

The graphs will be

  

Conclusion:

Hence,the inequalities are $10,000\le y\le 150,000$ and $1000\le x\le 17000$ and graph is drawn

(b)

To determine

To name: The possible solution

Answer to Problem 25PPS

The one possible solution is $\left(16000,10000\right)$

Explanation of Solution

Calculation:

From the graph

One possible solution will be $\left(16000,10000\right)$

Conclusion:

Hence,the one possible solution is $\left(16000,10000\right)$

(c)

To determine

To find: whether the given pair is a solution or not

Answer to Problem 25PPS

The given pair $\left(15000,30000\right)$ is not a solution

Explanation of Solution

Given:

  $\left(15000,30000\right)$

Calculation:

Here the solution is

  $\left(x,y\right)=\left(15000,30000\right)$

The point lies inside the said region

Therefore the point satisfies each inequality

Conclusion:

Hence,the given pair $\left(15000,30000\right)$ is a solution