MATH 8 Final Exam

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Shasta College *

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8

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Industrial Engineering

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Oct 30, 2023

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pdf

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7

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NAME:____________________________ Final Exam Show all work! 1. Using the Simplex method Maximize 𝑧 = 2𝑥 1 + 𝑥 2 + 𝑥 3 subject to the constraints { 4𝑥 1 + 12𝑥 2 + 𝑥 3 ≤ 124 8𝑥 1 + 5𝑥 3 ≤ 152 𝑥 1 ≥ 0, 𝑥 2 ≥ 0, 𝑥 3 ≥ 0
2. Solve by solving the dual problem. Minimize 𝑧 = 42𝑥 1 + 70𝑥 2 subject to { 5𝑥 1 + 4𝑥 2 ≥ 30 3𝑥 1 + 4𝑥 2 ≥ 22 𝑥 1 ≥ 0, 𝑥 2 ≥ 0
3. Using the Simplex method Maximize 𝑧 = 𝑥 1 − 2𝑥 2 subject to { 𝑥 1 + 𝑥 2 ≥ 10 2𝑥 1 + 5𝑥 2 ≤ 60 𝑥 1 ≥ 0, 𝑥 2 ≥ 0
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