Question

A zoo keeper wants to fence a rectangular habitat for goats. The length of the habitat should be at least 80 feet, and the perimeter of the habitat should be no more than 300 feet.

a. Write and graph a system of linear inequalities
b. Write two possible solutions

Answer 1

Let x ft be the lenght of the fence and y ft be the width of the fence.

1. The length of the habitat should be at least 80 feet, then

`x\ge 80\ ft.`

2. The perimeter of the habitat should be no more than 300 feet. The perimeter of the fenceis 2x+2y ft, then

`2x+2y\le 300\ ft.`

3. The system of inequalities that represent the model is

`\left\{\begin{array}{l}x\ge 80\\2x+2y\le 300\end{array}\right..`

The graph of these inequalities is attached.

Two possible solutions are

1. x=100 ft, y=20 ft (100≥80 and 2·100+2·20=240≤300);
2. x=110 ft, y=30 ft (110≥80 and 2·110+2·30=280≤300).