х+ 2y < 12 —х + у s 5 x+у < 5 х2 0, у 2 0. p = (х, у) %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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![**Objective:**
Maximize \( p = 2x + y \) subject to the following constraints:
1. \( x + 2y \leq 12 \)
2. \(-x + y \leq 5 \)
3. \( x + y \leq 5 \)
4. \( x \geq 0, \, y \geq 0 \)
**Solution:**
\[ p = \underline{\phantom{p = }} \]
\[ (x, y) = \left( \underline{\phantom{x}}, \underline{\phantom{y}} \right) \]
**Explanation:**
This is a linear programming problem where you aim to maximize the function \( p = 2x + y \) given the constraints listed. The constraints describe a feasible region on the coordinate plane, typically a polygon, and the goal is to find the values of \( x \) and \( y \) within this region that maximize the value of \( p \).
The solution involves finding the vertices of the feasible region created by the constraints and evaluating \( p \) at these points to find the maximum value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd05e9239-019a-4597-8fb6-f7e552204d4e%2Ffad8b946-16ea-491d-a9dd-7f6f7c0a3e60%2Flriwwrn_processed.png&w=3840&q=75)
Transcribed Image Text:**Objective:**
Maximize \( p = 2x + y \) subject to the following constraints:
1. \( x + 2y \leq 12 \)
2. \(-x + y \leq 5 \)
3. \( x + y \leq 5 \)
4. \( x \geq 0, \, y \geq 0 \)
**Solution:**
\[ p = \underline{\phantom{p = }} \]
\[ (x, y) = \left( \underline{\phantom{x}}, \underline{\phantom{y}} \right) \]
**Explanation:**
This is a linear programming problem where you aim to maximize the function \( p = 2x + y \) given the constraints listed. The constraints describe a feasible region on the coordinate plane, typically a polygon, and the goal is to find the values of \( x \) and \( y \) within this region that maximize the value of \( p \).
The solution involves finding the vertices of the feasible region created by the constraints and evaluating \( p \) at these points to find the maximum value.
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