Sample_Midterm_Problem

# Sample_Midterm_Problem - IEEM 202 Midterm (Fall 2004) Sheet...

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Unformatted text preview: IEEM 202 Midterm (Fall 2004) Sheet A Page 1 IEEM 202: Introduction to Operations Research, Fall 2004 Mid-Term Exam (Sheet A) Question 1. (30%) The feasible region of an LP is shown as the shadow area in the following figure. Suppose the objective of the LP is to maximize the sum of 4 x and y . 1) Write the formulation of the LP. (10%) 2) Identify the corner point that corresponds to the optimal solution. (10%) 3) Write the standard from of the LP. (10%) Solution: 1) LP: 7 28 7 4 4 ≥ ≤ + ≤ + − + = y y x y x to Subject y x Z Max 2) There are three corner points (-7,0),(7,0) and (21/11, 56/11). And the corner point that corresponds to the optimal solution is (7,0). 3)Let , , , ≥ − = − + − + x x x x x The standard form of the LP is: , , , 7 28 7 4 4 4 4 , 2 1 2 1 ≥ = + + − = + + + − + − = − + − + − + − + y s s x x s y x x s y x x to Subject y x x Z Max 7 4-7 7 y (1) (2) x IEEM 202 Midterm (Fall 2004) Sheet A Page 2 Question 2. (20%) Considering the following linear programming problem LP1: LP1: Max Z = -2X 1 +6X 2 Subject to X 1 +X 2 ≥ 2 -X 1 +X 2 ≤ 1 X 1 + 4X 3 = 9 X 1 ≥ 0, X 2 ≥ 0, X 3 is unrestricted (1)...
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## This note was uploaded on 01/05/2011 for the course IELM IELM202 taught by Professor D during the Fall '10 term at HKUST.

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Sample_Midterm_Problem - IEEM 202 Midterm (Fall 2004) Sheet...

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