Graph the first inequality subject to the nonnegative restrictions. 18x + 30y≤ 1800, x ≥ 0, y 20 Use the graphing tool to graph 18x + 30y≤ 1800 and the boundary lines representing the nonnegative constraints. Click to enlarge graph -500 -250 Ay 100- $0 -50 -100- 250 X 500 o Q
Graph the first inequality subject to the nonnegative restrictions. 18x + 30y≤ 1800, x ≥ 0, y 20 Use the graphing tool to graph 18x + 30y≤ 1800 and the boundary lines representing the nonnegative constraints. Click to enlarge graph -500 -250 Ay 100- $0 -50 -100- 250 X 500 o Q
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Graphing Inequalities Subject to Nonnegative Restrictions
**Problem Statement:**
Graph the first inequality subject to the nonnegative restrictions:
\[ 18x + 30y \leq 1800, \quad x \geq 0, \quad y \geq 0 \]
Use the graphing tool to graph the inequality \( 18x + 30y \leq 1800 \) and the boundary lines representing the nonnegative constraints.
**Instructions:**
1. Identify the boundary line for the inequality \( 18x + 30y = 1800 \).
2. Graph the corresponding inequality \( 18x + 30y \leq 1800 \) ensuring that the region satisfying the inequality is shaded.
3. Ensure that the graph includes the constraints \( x \geq 0 \) and \( y \geq 0 \), which restrict the feasible region to the first quadrant.
**Graph Analysis:**
- The graph shows a grid with the horizontal axis labeled \( x \) and the vertical axis labeled \( y \).
- The axes are scaled with intervals marking every 250 units.
- The positive quadrants are the focus for this graph due to the nonnegative constraints (\( x \geq 0 \) and \( y \geq 0 \)).
To graph \( 18x + 30y \leq 1800 \):
1. Rewrite the inequality in slope-intercept form if needed, or find the intercepts:
- For the \( x \)-intercept: Set \( y = 0 \) in \( 18x + 30y = 1800 \) to get \( x = 100 \).
- For the \( y \)-intercept: Set \( x = 0 \) in \( 18x + 30y = 1800 \) to get \( y = 60 \).
2. Plot these intercepts \((100, 0)\) and \((0, 60)\) on the graph.
3. Draw the boundary line through these intercepts.
4. Shade the region below the line to indicate \( 18x + 30y \leq 1800 \).
Remember to consider the nonnegative constraints \( x \geq 0 \) and \( y \geq 0 \), restricting the solution to the first quadrant.
**Helpful Hint:**
Util](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d9df1eb-9cbe-4888-87d6-c14249115dd3%2F4c6e6936-8665-43cc-8c26-27fb09684a7a%2Fiq6lh57_processed.png&w=3840&q=75)
Transcribed Image Text:### Graphing Inequalities Subject to Nonnegative Restrictions
**Problem Statement:**
Graph the first inequality subject to the nonnegative restrictions:
\[ 18x + 30y \leq 1800, \quad x \geq 0, \quad y \geq 0 \]
Use the graphing tool to graph the inequality \( 18x + 30y \leq 1800 \) and the boundary lines representing the nonnegative constraints.
**Instructions:**
1. Identify the boundary line for the inequality \( 18x + 30y = 1800 \).
2. Graph the corresponding inequality \( 18x + 30y \leq 1800 \) ensuring that the region satisfying the inequality is shaded.
3. Ensure that the graph includes the constraints \( x \geq 0 \) and \( y \geq 0 \), which restrict the feasible region to the first quadrant.
**Graph Analysis:**
- The graph shows a grid with the horizontal axis labeled \( x \) and the vertical axis labeled \( y \).
- The axes are scaled with intervals marking every 250 units.
- The positive quadrants are the focus for this graph due to the nonnegative constraints (\( x \geq 0 \) and \( y \geq 0 \)).
To graph \( 18x + 30y \leq 1800 \):
1. Rewrite the inequality in slope-intercept form if needed, or find the intercepts:
- For the \( x \)-intercept: Set \( y = 0 \) in \( 18x + 30y = 1800 \) to get \( x = 100 \).
- For the \( y \)-intercept: Set \( x = 0 \) in \( 18x + 30y = 1800 \) to get \( y = 60 \).
2. Plot these intercepts \((100, 0)\) and \((0, 60)\) on the graph.
3. Draw the boundary line through these intercepts.
4. Shade the region below the line to indicate \( 18x + 30y \leq 1800 \).
Remember to consider the nonnegative constraints \( x \geq 0 \) and \( y \geq 0 \), restricting the solution to the first quadrant.
**Helpful Hint:**
Util
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