hw1-sol - ISyE 6669 Homework 1 Solutions 3.3.1 AB is x1 x2...

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ISyE 6669 Homework 1 Solutions 3.3.1 AB is x 1 + x 2 = 4. CD is x 1 - x 2 = 5. From the graph, we see that there is no feasible solution (Case 3). 1

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3.3.2 AB is 8 x 1 + 2 x 2 = 16. CD is 5 x 1 + 2 x 2 = 12. Dotted line is z = 4 x 1 + x 2 = 4. Feasible region is bounded by AEDF. Since isoproﬁt line is parallel to AE, entire line segment AE is optimal. Thus, we have alternative or multiple optimal solutions. 3.3.3 AB is x 1 - x 2 = 4. AC is x 1 + 2 x 2 = 4. Feasible region is bounded by AC and inﬁnite segment AB. Dotted line is isoproﬁt line z = 0. To increase z, we move parallel to isoproﬁt 2
line in a upward and ’leftward’ direction. We will never entirely lose contact with the feasible region, so we have an unbounded LP (Case 4). 3.3.4 AB is 2 x 1 + x 2 = 6. CS is x 1 + 3 x 2 = 9. The feasible region is bounded by AECF. Dotted line is 3 = 3 X 1 + x 2 . Moving up and to right (and parallel to isoproﬁt line) we ﬁnd that point A is optimal. Thus, E has 2 x 1 + x 2 = 6 and x 2 = 0. Optimal solution to the LP is

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This note was uploaded on 12/30/2011 for the course ISYE 6669 taught by Professor Staff during the Fall '08 term at Georgia Tech.

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hw1-sol - ISyE 6669 Homework 1 Solutions 3.3.1 AB is x1 x2...

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