Solve this using the graphical method. Be sure to clearly show all steps: Sketch the feasible region Determine the corner points Determine the minimum of the objective function ●

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter5: Network Models
Section5.5: Shortest Path Models
Problem 30P
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### Linear Programming Problem

**Objective:**  
Minimize \( z = 3x + y \)

**Subject to:**
1. \( 3y + 5x \geq 30 \)
2. \( 6y + 4x \geq 40 \)
3. \( y + x \geq 8 \)
4. \( x \geq 0 \)
5. \( y \geq 0 \)

---

**Instructions:**

Solve this using the graphical method. Be sure to clearly show all steps:

1. **Sketch the feasible region**  
   Plot the given inequalities on the coordinate plane to determine the feasible region.

2. **Determine the corner points**  
   Identify the intersection points (corner points) of the constraints within the feasible region.

3. **Determine the minimum of the objective function**  
   Evaluate the objective function \( z = 3x + y \) at each corner point to find the minimum value.

---

**Task:**

- Sketch the feasible region
- Determine the corner points
- Determine the minimum of the objective function

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Transcribed Image Text:### Linear Programming Problem **Objective:** Minimize \( z = 3x + y \) **Subject to:** 1. \( 3y + 5x \geq 30 \) 2. \( 6y + 4x \geq 40 \) 3. \( y + x \geq 8 \) 4. \( x \geq 0 \) 5. \( y \geq 0 \) --- **Instructions:** Solve this using the graphical method. Be sure to clearly show all steps: 1. **Sketch the feasible region** Plot the given inequalities on the coordinate plane to determine the feasible region. 2. **Determine the corner points** Identify the intersection points (corner points) of the constraints within the feasible region. 3. **Determine the minimum of the objective function** Evaluate the objective function \( z = 3x + y \) at each corner point to find the minimum value. --- **Task:** - Sketch the feasible region - Determine the corner points - Determine the minimum of the objective function Upload a picture showing your work here: (Upload Button) Choose File (Button) No file chosen
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