Chapter 6, Problem 13CT

a.

To determine

the system of linear inequalities for the situation.

Answer to Problem 13CT

  $W \le 30\text{ and }L+W \le 90$

Explanation of Solution

Given:

The garden can be no more than 30 feet wide

Length of given wire is180 feet.

Formula used:

Perimeter of rectangle $=2\times \left(L+W\right)$

where $L=$ Length of rectangle and $W=$ Width of rectangle.

Calculation:

From the given information, the garden can be no more than 30 feet wide.

  $\Rightarrow W\le 30$

Now, for perimeter of rectangle,

  $\Rightarrow \text{Perimeter of rectangle}=2\times \left(L+W\right)$

Again the farmer use at most 180 feet of chicken wire,

Perimeter of rectangle $=2\times \left(L+W\right)$

  $\Rightarrow 2\times \left(L+W\right)\le 180$

  $\Rightarrow \left(L+W\right)\le \frac{180}{2}$

  $\Rightarrow \left(L+W\right)\le 90$

Conclusion:

Therefore, the system of linear inequalities for the situation is $W \le 30\text{ and }L+W \le 90.$

b.

To determine

To determine the graph of the system.

Explanation of Solution

Calculation for graph:

In equality there are multiple possible solutions, taking a simple solution.

From the previous sub part concluded inequality expression is, the system of linear inequalities for the situation is $W \le 30\text{ and }L+W \le 90.$

Now taking a value of $W =20\text{ and }L=10$

Values of W	Values of L	Values of perimeter
20	10	30

  $\Rightarrow L+W \le 90$

The value is $L+W=30$ which is $\le 90$ .

By taking different values, the graph can be plotted.

Graph:

  

Interpretation:

Therefore, the graph of the system with green shades and black boundary represents the possible solutions.