MthSc-813 Advanced Linear Programming Spring 1998
Midterm Exam
March 9, 1998
This take-home exam is due by 3:00 on Thursday, March 12, 1997. Sign and return
this cover sheet with your exam.
There are a total of 60 points. Point value is listed next to e
MthSc-813 Advanced Linear Programming Spring 1998
Midterm Exam
March 9, 1998
This take-home exam is due by 3:00 on Thursday, March 12, 1997. Sign and return
this cover sheet with your exam.
There are a total of 60 points. Point value is listed next to e
MthSc-813 Advanced Linear Programming Spring 1998
Midterm Exam
March 9, 1998
This take-home exam is due by 3:00 on Thursday, March 12, 1998. Sign and return
this cover sheet with your exam.
There are a total of 60 points. Point value is listed next to e
MthSc-813 Advanced Linear Programming Spring 1997
Final Exam
April 24, 1997
This take-home exam is due by 4:00 on Wednesday, April 29, 1998. Sign and
return this cover sheet with your exam to April Haynes.
There are a total of ? points. Point value is l
MthSc 813 Spring 1998
Homework 1 Key
February 14, 1998
Vanderbei 5.1 The general form problem is
max
cT x
subject to a Ax b
lxu
The dual of this problem is
min
bT v aT w + uT y lT z
subject to AT v AT w + Iy Iz = c
v, w, y, z 0
Vanderbei 5.2 The rst print
Mathematical Sciences 813
Homework 2 Solutions
Class Problem Show that a generalized halfspace is convex.
Let H = x R n : aT x b . We consider three cases:
a = 0: In this case, H is a regular halfspace and is convex.
a = 0, b 0: In this case, H = Rn and
Mathematical Sciences 813
Homework 3 Solutions
Class Problem Complete the proof of Hellys Theorem.
Lemma 1 If Ax b has no solution, then there exists a subsystem Ax with no solution,
b
consisting of at most n + 1 inequalities.
Proof WLOG, we can take m >