### Sketching the Feasible Region for Given InequalitiesTo determine the region that corresponds to the given inequalities, we'll follow these steps:1. **Identify the inequalities:** * $ x + y \geq 5 $ * $ x \leq 10 $ * $ y \leq 8 $ * $ x \geq 0 $ * $ y \geq 0 $2. **Graph each inequality on the coordinate plane:** - **Inequality 1: $ x + y \geq 5 $** - This represents the region above or on the line $ x + y = 5 $. - **Inequality 2: $ x \leq 10 $** - This represents the region to the left of or on the line $ x = 10 $. - **Inequality 3: $ y \leq 8 $** - This represents the region below or on the line $ y = 8 $. - **Inequality 4: $ x \geq 0 $** - This indicates the region to the right of or on the y-axis. - **Inequality 5: $ y \geq 0 $** - This indicates the region above or on the x-axis.3. **Determine the feasible region:** - The feasible region is the intersection of the areas defined by all given inequalities. - The points that define the corners (intersection points) of this region are the vertices.4. **Find the vertices:** - Set up each pair of equations to determine intersection points: - $ x + y = 5 $ and $ x = 0 $: $ (0, 5) $ - $ x + y = 5 $ and $ y = 0 $: $ (5, 0) $ - $ x + y = 5 $ and $ x = 10 $: $ (10, -5) $ - $ x + y = 5 $ and $ y = 8 $: $ (-3, 8) $ - $ y = 8 $ and $ x = 10 $: $ (10, 8) $ - Note that some intersection

*Concept:- draw the graph, by finding the intercepts. for x+y = 5, put x = 0, we will get y = 5 put…

Answered: Sketch the region that corresponds to…

Sketch the region that corresponds to the given inequalities, say whether the region is bounded or unbounded, and find the coordinates of all corner points (if any). x + y 2 5 < 10 y< 8 x> 0, y > 0

Intermediate Algebra

10th Edition

ISBN:9781285195728

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter7: Equations And Inequalities In Two Variables

Section7.2: Linear Inequalities In Two Variables

Problem 37.3PS

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

### Sketching the Feasible Region for Given Inequalities

To determine the region that corresponds to the given inequalities, we'll follow these steps:

1. **Identify the inequalities:**
* $ x + y \geq 5 $
* $ x \leq 10 $
* $ y \leq 8 $
* $ x \geq 0 $
* $ y \geq 0 $

2. **Graph each inequality on the coordinate plane:**
- **Inequality 1: $ x + y \geq 5 $**
- This represents the region above or on the line $ x + y = 5 $.
- **Inequality 2: $ x \leq 10 $**
- This represents the region to the left of or on the line $ x = 10 $.
- **Inequality 3: $ y \leq 8 $**
- This represents the region below or on the line $ y = 8 $.
- **Inequality 4: $ x \geq 0 $**
- This indicates the region to the right of or on the y-axis.
- **Inequality 5: $ y \geq 0 $**
- This indicates the region above or on the x-axis.

3. **Determine the feasible region:**
- The feasible region is the intersection of the areas defined by all given inequalities.
- The points that define the corners (intersection points) of this region are the vertices.

4. **Find the vertices:**
- Set up each pair of equations to determine intersection points:
- $ x + y = 5 $ and $ x = 0 $: $ (0, 5) $
- $ x + y = 5 $ and $ y = 0 $: $ (5, 0) $
- $ x + y = 5 $ and $ x = 10 $: $ (10, -5) $
- $ x + y = 5 $ and $ y = 8 $: $ (-3, 8) $
- $ y = 8 $ and $ x = 10 $: $ (10, 8) $
- Note that some intersection

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