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Max P = 4x+2y Subject to: x+2y ≤ 10 x+4y ≤ 12 x≥0, y 20

Max P = 4x+2y Subject to: x+2y ≤ 10 x+4y ≤ 12 x≥0, y 20

Advanced Engineering Mathematics
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 \( P = 4x + 2y \) **Subject to the Constraints:** 1. \( x + 2y \leq 10 \) 2. \( x + 4y \leq 12 \) 3. \( x \geq 0, \, y \geq 0 \) These constraints define a feasible region in the first quadrant of the Cartesian plane, bounded by the lines \( x + 2y = 10 \) and \( x + 4y = 12 \), along with the x and y axes. The goal is to find values for \( x \) and \( y \) that maximize the objective function \( P \) while remaining within the feasible region.
Transcribed Image Text:### Linear Programming Problem **Objective:** Maximize \( P = 4x + 2y \) **Subject to the Constraints:** 1. \( x + 2y \leq 10 \) 2. \( x + 4y \leq 12 \) 3. \( x \geq 0, \, y \geq 0 \) These constraints define a feasible region in the first quadrant of the Cartesian plane, bounded by the lines \( x + 2y = 10 \) and \( x + 4y = 12 \), along with the x and y axes. The goal is to find values for \( x \) and \( y \) that maximize the objective function \( P \) while remaining within the feasible region.
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