Chapter 3.2, Problem 18PPS

To determine

To Find: The vertices of the triangle formed by the system of inequalities $x\ge 0,y\ge 0\text{and x+2y < 4}$

Answer to Problem 18PPS

  $\left(0,0\right),\left(0,2\right)\text{ and }\left(4,0\right)$

Explanation of Solution

Given

Given inequalities are.

  $x\ge 0,y\ge 0\text{and x+2y < 4}$ .

Calculation:

Drawing the graph of inequality $x\ge 0$ .

Shade the region right of the y-axis.

Drawing the graph of inequality $y\ge 0$ .

Shade the region above x-axis.

Drawing the graph of inequality $x+2y<4$ .

  $\begin{array}{l}x+2y<4\\ 2y<4-x\\ y<2-\frac{x}{2}\end{array}$

Plot the coordinates of equation $y=2-\frac{x}{2}$ .

  $\begin{array}{cc}x& y\\ 0& 2\\ 4& 0\end{array}$

Shade the region below the line as $y<2-\frac{x}{2}$ .

  

From the above graph, vertices of triangle formed are $\left(0,0\right),\left(0,2\right)\text{ and }\left(4,0\right)$

So,the answer is $\left(0,0\right),\left(0,2\right)\text{ and }\left(4,0\right)$