Linear Optimization Quiz 1
Fall 2016
Score:
/18
Name: W
1. Consider the following linear programining problemi Maximize: 2:131 + 3:132
!
l
l
Subject to: :r1 + 1:2 3 4
171 + 1'72 S 6
$1731.? 2 0
(a) (t
Linear Optimization Test # ' Name= m
Fall 2016 . ,
Score: / 30
I
l
1.(5pts) Consider the folloizving LP: inimize: :1 + m2 :53
! Subject to: 51:1 ~ $2 + 2x3_ < 5
I ~21L'1 + 31152 - 123_ 1
i :31 > 0,
Linear Optimization ~ Test 2 i . Name: -%M
October 2E, 2016 I
Score: /30 '
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1. Write the dual of each of [the1followiu g LPS. No explanation is required, but if you do any
intermediate work be sure,t
Linear Optimization Assignment #3
Solutions
1. e, a, b, d, f, g, c
2. (a)
b
a
r
s
g
d
(b) (r,d, b, a, g, s)
(c) We can push an additional flow of one all along the path (r, d, b, a, g, s) in G. For
ea
Linear Optimization Assignment #2
Solutions
1. (a) Every feasible solution to this IP is a (0,1)-vector, since x 1, x is integral, and if
xM > 1 for any value of M , it could not satisfy any constrain
Linear Optimization Assignment #3
Due: At the beginning of class on Friday, December 2nd.
1. Give a topological sort of the following digraph, or explain why none exists.
c
b
g
a
d
e
f
2. Consider the
Linear Optimization Assignment #2
Due: At the beginning of class on Wednesday, November 9th.
1. Let G be a graph. A matching in G is a set of edges, none of which meet at a vertex. Let M
denote the se
Linear Optimization Assignment #1
Due: At the beginning of class on Friday, October 7th.
As a reminder, here is a statement from our course outline:
In this class, students are allowed (and encouraged