lem. |Y2 |Y2 riables of x, and x2, write the initial system for the dual problem. plex tableau for the dual problem. 1 X2 P
lem. |Y2 |Y2 riables of x, and x2, write the initial system for the dual problem. plex tableau for the dual problem. 1 X2 P
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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4.
![**Transcription for Educational Website**
Minimize \( C = 7x_1 + 2x_2 \)
Subject to:
- \( 2x_1 + 7x_2 \geq 5 \)
- \( 7x_1 + 8x_2 \geq 3 \)
- \( x_1, x_2 \geq 0 \)
---
**a. Form the dual problem.**
Maximize \( P = [ \text{blank} ] y_1 + [ \text{blank} ] y_2 \)
Subject to:
- \( y_1 + y_2 \leq [ \text{blank} ] \)
- \( [ \text{blank} ] y_1 + [ \text{blank} ] y_2 \leq [ \text{blank} ] \)
- \( y_1, y_2 \geq 0 \)
---
**b. Using the slack variables of \( x_1 \) and \( x_2 \), write the initial system for the dual problem.**
1. \( y_1 + [ \text{blank} ] y_2 + x_1 = [ \text{blank} ] \)
2. \( y_1 + [ \text{blank} ] y_2 + x_2 = [ \text{blank} ] \)
3. \( y_1 + y_2 + P = 0 \)
---
**c. Fill in the initial simplex tableau for the dual problem.**
| | \( y_1 \) | \( y_2 \) | \( x_1 \) | \( x_2 \) | \( P \) |
|-------|-----------|-----------|-----------|-----------|-------|
| \( x_1 \) | [ \text{blank} ] | [ \text{blank} ] | [ \text{blank} ] | [ \text{blank} ] | [ \text{blank} ] |
| \( x_2 \) | [ \text{blank} ] | [ \text{blank} ] | [ \text{blank} ] | [ \text{blank} ] | [ \text{blank} ] |
| \( P \) | [ \text{blank} ] | [ \text{blank} ] | [ \text{blank} ] |](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5af4684-8c2d-4df0-9359-946952989e9a%2F81aa5df2-9f33-491f-8025-e6ae5db2f940%2F02ucxp5_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website**
Minimize \( C = 7x_1 + 2x_2 \)
Subject to:
- \( 2x_1 + 7x_2 \geq 5 \)
- \( 7x_1 + 8x_2 \geq 3 \)
- \( x_1, x_2 \geq 0 \)
---
**a. Form the dual problem.**
Maximize \( P = [ \text{blank} ] y_1 + [ \text{blank} ] y_2 \)
Subject to:
- \( y_1 + y_2 \leq [ \text{blank} ] \)
- \( [ \text{blank} ] y_1 + [ \text{blank} ] y_2 \leq [ \text{blank} ] \)
- \( y_1, y_2 \geq 0 \)
---
**b. Using the slack variables of \( x_1 \) and \( x_2 \), write the initial system for the dual problem.**
1. \( y_1 + [ \text{blank} ] y_2 + x_1 = [ \text{blank} ] \)
2. \( y_1 + [ \text{blank} ] y_2 + x_2 = [ \text{blank} ] \)
3. \( y_1 + y_2 + P = 0 \)
---
**c. Fill in the initial simplex tableau for the dual problem.**
| | \( y_1 \) | \( y_2 \) | \( x_1 \) | \( x_2 \) | \( P \) |
|-------|-----------|-----------|-----------|-----------|-------|
| \( x_1 \) | [ \text{blank} ] | [ \text{blank} ] | [ \text{blank} ] | [ \text{blank} ] | [ \text{blank} ] |
| \( x_2 \) | [ \text{blank} ] | [ \text{blank} ] | [ \text{blank} ] | [ \text{blank} ] | [ \text{blank} ] |
| \( P \) | [ \text{blank} ] | [ \text{blank} ] | [ \text{blank} ] |
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