MATH 407
MIDTERM EXAM
Wednesday, October 28, 2015
MIDTERM EXAM GUIDE
Calculators are not allowed for this exam. The exam will consist of 5 questions. The midterm is worth a total
of 250 points. The content of each question and its point value is listed be
1
Solutions to homework 5
1. Let A Rmn and
M
A
I
=
R(mn)n
Let vi denote the i-th row of the matrix M and S cfw_1, . . . , m + n. Show
that c Cone(vi | i S ) if and only if c = AT y r for some y
0
and r
0 with yi = 0 if i S cfw_1, . . . , m and rj = 0 if
Solutions to Homework 3
The following is Question 4 from
http:/www.math.washington.edu/burke/crs/407/suppl/simplex2.pdf
Solve the following LP using the two-phase simplex algorithm
maximise
subject to
x1
+ x2 + x3
2 3
1
x1
1
3 1 x 2
2 1 3
x3
Solution:
Solutions to Homework 4
The following is Question 4 from
http:/www.math.washington.edu/burke/crs/407/suppl/cs.pdf
T
Is x = (0, 0, 0, 0, 0, 10) optimal for the following LP P :
maximise
subject to
T
cT x
Ax
b, x
0
T
where c = (2, 4, 1, 0, 6, 8) , b = (10,
Homework 2
Due 16th of July 2013
1. Review linear algebra
http:/www.math.washington.edu/burke/crs/407/308rev/
2. http:/www.math.washington.edu/burke/crs/407/models/m12.html
3. http:/www.math.washington.edu/burke/crs/407/models/m6.html
1
Homework 4
Due 8th of August 2013
1. Do questions 4 and 7
http:/www.math.washington.edu/burke/crs/407/suppl/cs.pdf
2. Do questions 2 and 3
http:/www.math.washington.edu/burke/crs/407/suppl/computedual.pdf
3. Do question 2 from
http:/www.math.washington.ed
Due 1st of August
1. Review the example on the two phase simplex algorithm in Section 3.2 of
http:/www.math.washington.edu/burke/crs/407/notes/section3.pdf
This is the same example I partially wrote down in class.
2. Do questions 4 and 5 from
http:/www.ma
Homework 1
Due 9th of July 2013
1. Review week 1 lectures.
http:/www.math.washington.edu/burke/crs/407/notes/section1.pdf
2. Questions 1 (b) and (c) from
http:/www.math.washington.edu/burke/crs/407/suppl/2dLPs.pdf
For 1 (a) formulate the dual LP.
3. http:
Homework 5
Due 15th of August 2013
1. Let A Rmn and
M
=
A
In
R(mn)n
Let vi denote the i-th row of the matrix M and S cfw_1, . . . , m + n. Show
that c Cone(vi | i S) if and only if c = AT y r for some y
0
and r
0 with yi = 0 if i S cfw_1, . . . , m and r