I nees help on this practice problem. ### Problem 4: Linear Programming Problem (LPP) in 2 Dimensions**Objective:**- You are working with a 2-D Linear Programming Problem that has four constraints. The image illustrates a region that satisfies the first three constraints. Your tasks are as follows: - Draw into the diagram the line for the fourth constraint: $ x - 12y \geq 0 $. - Shade the Feasible Region. - Calculate and label the new corner points after incorporating the fourth constraint.**Diagram Description:**- **Triangle Vertices:** - The diagram is a triangle with the following labeled vertices: - $ (10,0) $ - $ (19, \frac{9}{2}) $ - $ (25,2) $### Steps:1. **Adding the Fourth Constraint:** - Begin by plotting the line for $ x - 12y = 0 $. Transform this into $ y = \frac{x}{12} $. - This line will intersect the x-axis and will help bisect the plane into regions.2. **Shading the Feasible Region:** - Determine which side of the line satisfies $ x - 12y \geq 0 $ by testing a point not on the line (commonly the origin $ (0,0) $ is used unless it lies on the boundary). - Shade the region that meets all constraints, including the new line you just added.3. **Calculating New Corner Points:** - Examine where the new line intersects the existing boundaries of the triangle to find any new corner points. - Adjust and label these points accordingly, ensuring they all satisfy the four constraints.This exercise enhances understanding of constraint application in optimization problems and visualizing feasible regions on a 2-D plane.

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Description: I nees help on this practice problem. ### Problem 4: Linear Programming Problem (LPP) in 2 Dimensions**Objective:**- You are working with a 2-D Linear Programming Problem that has four constraints. The image illustrates a region that satisfies the fi

The given region of points that satisfies the first three constraints is,

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I am working with a 2-D LPP that has four constraints. Below is the region of points that satisfy the first three constraints. • Draw into the diagram the line for the fourth constraint: x – 12y > 0; • Shade the Feasible Region; and • Calculate and label the new corner points. (*.4) (25,2) (10,0)

I am working with a 2-D LPP that has four constraints. Below is the region of points that satisfy the first three constraints. • Draw into the diagram the line for the fourth constraint: x – 12y > 0; • Shade the Feasible Region; and • Calculate and label the new corner points. (*.4) (25,2) (10,0)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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I nees help on this practice problem.

### Problem 4: Linear Programming Problem (LPP) in 2 Dimensions

**Objective:**
- You are working with a 2-D Linear Programming Problem that has four constraints. The image illustrates a region that satisfies the first three constraints. Your tasks are as follows:

- Draw into the diagram the line for the fourth constraint: $ x - 12y \geq 0 $.
- Shade the Feasible Region.
- Calculate and label the new corner points after incorporating the fourth constraint.

**Diagram Description:**

- **Triangle Vertices:**
- The diagram is a triangle with the following labeled vertices:
- $ (10,0) $
- $ (19, \frac{9}{2}) $
- $ (25,2) $

### Steps:

1. **Adding the Fourth Constraint:**
- Begin by plotting the line for $ x - 12y = 0 $. Transform this into $ y = \frac{x}{12} $.
- This line will intersect the x-axis and will help bisect the plane into regions.

2. **Shading the Feasible Region:**
- Determine which side of the line satisfies $ x - 12y \geq 0 $ by testing a point not on the line (commonly the origin $ (0,0) $ is used unless it lies on the boundary).
- Shade the region that meets all constraints, including the new line you just added.

3. **Calculating New Corner Points:**
- Examine where the new line intersects the existing boundaries of the triangle to find any new corner points.
- Adjust and label these points accordingly, ensuring they all satisfy the four constraints.

This exercise enhances understanding of constraint application in optimization problems and visualizing feasible regions on a 2-D plane.

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