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Midterm Operations Research Review, Exercises of Operational Research

American University of BeirutOperational Research

Midterm Exam review exercises regrading Duality, Simplex Method, Revised Simplex Method and solving LPs graphically

Typology: Exercises

2018/2019
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Uploaded on 11/19/2019

vmorcos
vmorcos 🇱🇧

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Problem 1
Problem 2
Given the following LP:
(𝑃)max 𝑍 = 𝑐𝑥
𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜
𝐴𝑥 ≤ 𝑏
𝑥 ≥ 0
The dual is given by:
(𝐷)min
𝑤 = 𝑦𝑏
𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜
𝑦𝐴 ≥ 𝑐
𝑦 ≥ 0
Show the following:
(i) If (P) is unbounded then (D) is infeasible
(ii) If (D) is unbounded then (P) is infeasible
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Problem 2

Given the following LP:

(𝑃) max 𝑍 = 𝑐𝑥 𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝐴𝑥 ≤ 𝑏 𝑥 ≥ 0 The dual is given by: (𝐷) min 𝑤 = 𝑦𝑏 𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑦𝐴 ≥ 𝑐 𝑦 ≥ 0 Show the following: (i) If (P) is unbounded then (D) is infeasible (ii) If (D) is unbounded then (P) is infeasible