Graph the inequality subject to the nonnegative restrictions. 15x-24y <0, x ≥ 0, y ≥0 Use the graphing tool to graph the inequality and the boundary lines representing the nonnegative constraints. Click to enlarge graph -12-10 Ay 12- 10- 8- 6- -10- 10 12 A

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question

24

### Graphing Inequalities with Nonnegative Constraints

#### Objective:
Graph the inequality subject to the nonnegative restrictions given.

\[ 15x - 24y < 0, \quad x \geq 0, \quad y \geq 0 \]

#### Instructions:

1. **Identify the Inequality:**
   The inequality to be graphed is:
   \[ 15x - 24y < 0 \]

2. **Nonnegative Restrictions:**
   The graph must only show the area where:
   \[ x \geq 0 \]
   \[ y \geq 0 \]

3. **Graphical Representation:**
   - On the right, there is a graph with \(x\)-axis and \(y\)-axis ranging from -12 to 12.
   - Use the graph to accurately represent the inequality.

4. **Steps to Graph:**
   - **Boundary Line:** Start by graphing the boundary line where \( 15x - 24y = 0 \). This can be rewritten to \( y = \frac{15}{24}x \) or \( y = \frac{5}{8}x \).
   - **Shading the Region:** Since we have \( 15x - 24y < 0 \), shade the region below the boundary line because the inequality is less than 0.
   - **Nonnegative Constraints:** Ensure that the shaded region is only in the first quadrant where both \( x \) and \( y \) are nonnegative.

#### Visual Tool:
- **Graphing Tool:** 
  - A clickable graphing tool icon is available to enlarge the graph for more detailed analysis.
  
  ![Graphing Tool Icon](image link)

5. **Interactive Activity:**
   - Use the provided graphing tool to plot the boundary line and indicate the correct shaded region compliant with the inequality and constraints.
Transcribed Image Text:### Graphing Inequalities with Nonnegative Constraints #### Objective: Graph the inequality subject to the nonnegative restrictions given. \[ 15x - 24y < 0, \quad x \geq 0, \quad y \geq 0 \] #### Instructions: 1. **Identify the Inequality:** The inequality to be graphed is: \[ 15x - 24y < 0 \] 2. **Nonnegative Restrictions:** The graph must only show the area where: \[ x \geq 0 \] \[ y \geq 0 \] 3. **Graphical Representation:** - On the right, there is a graph with \(x\)-axis and \(y\)-axis ranging from -12 to 12. - Use the graph to accurately represent the inequality. 4. **Steps to Graph:** - **Boundary Line:** Start by graphing the boundary line where \( 15x - 24y = 0 \). This can be rewritten to \( y = \frac{15}{24}x \) or \( y = \frac{5}{8}x \). - **Shading the Region:** Since we have \( 15x - 24y < 0 \), shade the region below the boundary line because the inequality is less than 0. - **Nonnegative Constraints:** Ensure that the shaded region is only in the first quadrant where both \( x \) and \( y \) are nonnegative. #### Visual Tool: - **Graphing Tool:** - A clickable graphing tool icon is available to enlarge the graph for more detailed analysis. ![Graphing Tool Icon](image link) 5. **Interactive Activity:** - Use the provided graphing tool to plot the boundary line and indicate the correct shaded region compliant with the inequality and constraints.
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