Use the simplex method to find the optimal solution. Assume all variables are nonnegative.
Use the simplex method to find the optimal solution. Assume all variables are nonnegative.
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 am not sure how to solve these two, especially using the simple method? Can someone help!
![### Problem 6: HARMATHAP12 4.5.015
**Objective:**
Use the simplex method to find the optimal solution. Assume all variables are nonnegative.
**Minimization Problem:**
Minimize \( f = 3x + 2y \)
**Subject to the Constraints:**
- \(-x + y \leq 15\)
- \(x + y \geq 35\)
- \(x + y \leq 45\)
**Variables to Determine:**
- \(x = \) [input area]
- \(y = \) [input area]
- \(f = \) [input area]
### Problem 7: HARMATHAP12 4.5.020
**Objective:**
Use the simplex method or Excel. Assume that all variables are nonnegative.
**Maximization Problem:**
Maximize \( f = -x + 3y + 4z \)
**Subject to the Constraints:**
- \(x + y + z \leq 40\)
- \(-x + y + z \geq 30\)
- \(x + y - z \geq 20\)
**Variables to Determine:**
- \(x = \) [input area]
- \(y = \) [input area]
- \(z = \) [input area]
- \(f = \) [input area]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7878796-4071-4397-9fae-1cbeb3b69837%2Fc8fbbe3a-057d-41a1-b7f5-a78268b5da83%2F60y7uri_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 6: HARMATHAP12 4.5.015
**Objective:**
Use the simplex method to find the optimal solution. Assume all variables are nonnegative.
**Minimization Problem:**
Minimize \( f = 3x + 2y \)
**Subject to the Constraints:**
- \(-x + y \leq 15\)
- \(x + y \geq 35\)
- \(x + y \leq 45\)
**Variables to Determine:**
- \(x = \) [input area]
- \(y = \) [input area]
- \(f = \) [input area]
### Problem 7: HARMATHAP12 4.5.020
**Objective:**
Use the simplex method or Excel. Assume that all variables are nonnegative.
**Maximization Problem:**
Maximize \( f = -x + 3y + 4z \)
**Subject to the Constraints:**
- \(x + y + z \leq 40\)
- \(-x + y + z \geq 30\)
- \(x + y - z \geq 20\)
**Variables to Determine:**
- \(x = \) [input area]
- \(y = \) [input area]
- \(z = \) [input area]
- \(f = \) [input area]
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