Chapter 11: Q. 50 (page 783)

In Problems 43–52, graph each system of linear inequalities by hand. Tell whether the graph is bounded or unbounded, and label the corner points
$50 . \{\begin{cases} x \geq 0 \\ y \geq 0 \\ x + y \geq 2 \\ x + y \leq 8 \\ x + 2 y \geq 1 \end{cases}$

Short Answer

Expert verified

The shaded region shows the bounded region

Step by step solution

Step 1. Given information

Consider the first inequality in the system of inequalities is $x \geq 0$ & $y \geq 0$

we get the shaded region

Step 2. Consideration of third inequality

$x + y \geq 2$ , the equation of the equality consider by replacing with equality $x + y = 2$

For determining the shaded portion we use to test a point with $(0, 0)$

$0 + 0 \geq 2 0 \geq 2$

The shaded part does not include the point $(0, 0)$

Step 3. Consideration of fourth inequality

$x + y \leq 8$ ,the equation of line is replacing by inequality with equality $x + y = 8$

By substituting by test point $(0, 0)$

The point $(0, 0)$ contains the shaded portion in the equation $x + y \leq 8$

Step 4. Consideration of fourth inequality

$x + 2 y \geq 1$ , the equation of line is by replacing inequality with $x + 2 y = 1$

By using testing point $(0, 0)$ in inequality $x + 2 y \geq 1$

$0 + 0 \geq 1 0 \geq 1$

The shaded part does not includes the test point $(0, 0)$ in the inequality $x + 2 y \geq 1$

Step 5. Solution

The shaded portion is the bounded by all inequalities

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In Problems 43–52, graph each system of linear inequalities by hand. Tell whether the graph is bounded or unbounded, and label the corner points
$50 . \{\begin{cases} x \geq 0 \\ y \geq 0 \\ x + y \geq 2 \\ x + y \leq 8 \\ x + 2 y \geq 1 \end{cases}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Consideration of third inequality

Step 3. Consideration of fourth inequality

Step 4. Consideration of fourth inequality

Step 5. Solution

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In Problems 43–52, graph each system of linear inequalities by hand. Tell whether the graph is bounded or unbounded, and label the corner points50.x≥0y≥0x+y≥2x+y≤8x+2y≥1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Consideration of third inequality

Step 3. Consideration of fourth inequality

Step 4. Consideration of fourth inequality

Step 5. Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Discrete Mathematics

Geometry

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

In Problems 43–52, graph each system of linear inequalities by hand. Tell whether the graph is bounded or unbounded, and label the corner points
$50 . \{\begin{cases} x \geq 0 \\ y \geq 0 \\ x + y \geq 2 \\ x + y \leq 8 \\ x + 2 y \geq 1 \end{cases}$