Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Minimize c = x + y subject to x + 2y 2 9 2x + yz 9 x 2 0, y 2 0. C = (х,у) %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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## Linear Programming Problem

### Problem Statement:

Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. 

**HINT**: [See Example 1.] 
- Enter **EMPTY** if the region is empty.
- Enter **UNBOUNDED** if the function is unbounded.

### Objective:

Minimize \( c = x + y \) subject to the constraints:

1. \( x + 2y \geq 9 \)
2. \( 2x + y \geq 9 \)
3. \( x \geq 0, \, y \geq 0 \)

---

### Input Fields:

- **c =** [  ________  ]

- **\( (x, y) = \)** ( [ ________ ] )

---

This problem requires finding the values of \( x \) and \( y \) that minimize the objective function \( c = x + y \) while satisfying the given constraints.
Transcribed Image Text:## Linear Programming Problem ### Problem Statement: Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. **HINT**: [See Example 1.] - Enter **EMPTY** if the region is empty. - Enter **UNBOUNDED** if the function is unbounded. ### Objective: Minimize \( c = x + y \) subject to the constraints: 1. \( x + 2y \geq 9 \) 2. \( 2x + y \geq 9 \) 3. \( x \geq 0, \, y \geq 0 \) --- ### Input Fields: - **c =** [ ________ ] - **\( (x, y) = \)** ( [ ________ ] ) --- This problem requires finding the values of \( x \) and \( y \) that minimize the objective function \( c = x + y \) while satisfying the given constraints.
Expert Solution
Step 1

We will find the solution of the given linear programming problem by graphical method as it is a problem of two variables.

 MIN c = x + ysubject to       x + 2 y 9      2 x + y 9 and x,y0

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