Maximize p = 5x – 4y + 3z subject to 10x + 10z< 100 5y - 5z< 50 10x - 5ys 50 x 2 0, y 2 0, z > 0. p= (х, у, 2)%3D
Maximize p = 5x – 4y + 3z subject to 10x + 10z< 100 5y - 5z< 50 10x - 5ys 50 x 2 0, y 2 0, z > 0. p= (х, у, 2)%3D
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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![### Linear Programming Problem
**Objective:**
Maximize the function \( p = 5x - 4y + 3z \)
**Subject to the constraints:**
1. \( 10x + 10z \leq 100 \)
2. \( 5y - 5z \leq 50 \)
3. \( 10x - 5y \leq 50 \)
4. \( x \geq 0, \, y \geq 0, \, z \geq 0 \)
**Goal:**
- Find the maximum value of \( p \) and the corresponding values of \( x \), \( y \), and \( z \).
**Solutions should be input into the provided boxes:**
- Maximum value of \( p \) = [Input Box]
- Optimal solution \( (x, y, z) = \) [Input Box]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd05e9239-019a-4597-8fb6-f7e552204d4e%2F0c1de6d4-cde1-47b1-a589-9713f1b286bf%2Fjrbg0v_processed.png&w=3840&q=75)
Transcribed Image Text:### Linear Programming Problem
**Objective:**
Maximize the function \( p = 5x - 4y + 3z \)
**Subject to the constraints:**
1. \( 10x + 10z \leq 100 \)
2. \( 5y - 5z \leq 50 \)
3. \( 10x - 5y \leq 50 \)
4. \( x \geq 0, \, y \geq 0, \, z \geq 0 \)
**Goal:**
- Find the maximum value of \( p \) and the corresponding values of \( x \), \( y \), and \( z \).
**Solutions should be input into the provided boxes:**
- Maximum value of \( p \) = [Input Box]
- Optimal solution \( (x, y, z) = \) [Input Box]
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