Assigned:
Wednesday, September 22, 2004
Due:
Wednesday, September 29, 2004, at the beginning of class
General Instructions
- Please review the
course information.
- You must write down with whom you worked on the assignment. If this
changes from problem to problem, then you should write down this
information separately with each problem.
- Numbered problems are all from the textbook Introduction to
Mathematical Programming, 4th Edition.
Problems
- p. 92, Problem A2. Formulate but do not solve the LP.
- p. 93, Problem A9. Formulate but do not solve the LP.
- p. 139, Problem A3. Give a table and a graph like the one done
in class.
- Lenny Arprogram proposes the following method for solving a linear
program that has n variables and n constraints. First, express the linear
program as a system
A x <= b,
where A is an n by n matrix and x and b are
n dimensional vectors.
Next, left multiply both sides of the equation by A-1 (you can assume that A-1 exists) , giving
A-1 A x <= A-1 b
which is the same as
x <= A-1 b .
Now A-1 b is just a vector of numbers, so we can read off the solution.
Is Lenny correct? Either prove that Lenny is correct, or give a
counterexample.
- p. 149, problem A2.
- Extra Credit: Put the following problem into standard LP form.
(Hint: you may need to introduce a dummy variable.)
min |
| x - 1 | |
+ |
y |
|
|
s.t. |
x |
+ |
y |
<= |
17 |
|
3x |
- |
2y |
>= |
5 |
|
|
|
x,y |
>= |
0 |
Switch to:
cliff@ieor.columbia.edu