M
ASSACHUSETTS
I
NSTITUTE OF
T
ECHNOLOGY
15.053 – Optimization Methods in Management Science (Spring 2007)
Recitation 4, March 1
st
and March 2
nd
, 2007
Problem 1: More Simplex Tableau
Suppose while solving a maximization problem we obtain the following tableau, with the
basic variables highlighted in blue:
z
x
1
x
2
x
3
x
4
x
5
rhs
1
a
c
0
3
0
10
0
0
d
0
4
1
5
0
1
5
0
1
0
b
0
0
e
1
2
0
3
Give conditions on the missing values
a, b, c, d, e
and required to make the each of the
following statements true:
Part A:
What is the current solution?
Part B:
The current tableau represents a basic feasible solution in canonical form.
Part C:
The current tableau is optimal and multiple optimal solutions exist.
Part D:
The current basic solution is a degenerate basic feasible solution.
Part E:
The current basic solution is feasible, but the objective function value can be improved
by bringing
x
2
into the basis and pivoting
x
3
out.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentPart F:
There exists an extreme ray of optimal solutions
Part G:
The current solution is both optimal and degenerate and there exists an extreme ray of
optimal solutions
Part H:
Suppose a=0, d=e=2, and c=2 perform a pivot in terms of the variables.
Problem 2: March Madness
The NCAA is making plans for distributing tickets to the upcoming regional basketball
championships.
Up to 10,000 available seats will be divided between the media, the
competing universities, and the general public, subject to the following conditions:
o
Media people are admitted free, and at least 1000 tickets must be reserved for the
media.
o
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '07
 JamesOrli
 Management, Optimization, optimal solution, NCAA, sensitivity report, allowable decrease, demand limit

Click to edit the document details