. E.~-~A":L\.mm. i- . .
m-r' .=
"x
M H w 799: < r
it?" New
2
(r if i r: i. get? El it?" WW
Final Exam, 550.361 optimizationnaiweeniengggggg
Problem 1: Consider the max ow instance G = (V, E), 3,15 65 V, p: : E % R29 displayed in the
gure below, and th
Final Exam, 550.361 Optimization, Fall 2011\ t fi
Blank answers to a complete probiem will be awarded 20% of the credit. This is in contrast to
fundamentally incorrect answers, which wiil be awarded 0% of the credit.
Problem 1: Consider the foilowing line
Exam 2, 550.361 Optimization, Fall 2010 W
. Problem 1: (20 points) After a particular iteration of Dijkstras Aigorithrn, the programs
variable values are as indicated in the table below (on the left side). Fill out the next table (below,
on the right side
LA
Exam 2, 550.861 Optimization; Fall 2011 \Mmgg
Problem 1: (15 points) Consider the following linear program:
. . . . .mm 2m1.+g$2m33n .
st. 6m1~ 2.122 + 2% r: 4
m3m1 + 3322 + 2563 := 3
m1, m2, m3 2 0
You went to solve it with the Primal Simplex Method,
Exam 1, 550.361 Optimization, Fall 2011
Problem 1: SuppOse you are solving a iinear program via the Simplex Method3 and at some
point of this procedure the following Simplex tableau is the current tabieau:
1 6 4 3 6 O O U 22
cfw_l i 3 l 4 O O 2 9
cfw_
Exam 1, 550.361 Optimization, Fall 2010
Problem 1: Suppose that you are in the middle of executing the Simplex Algorithm on the linear
program LP (say the variables are 331, :52, 533, $4, 555, $5,237), and you have the current tableau:
3 1
7 0
2
550.361 Optimization, Exam 2, Fall 2012
Problem 1: Consider the following linear program:
min 4x1 x2 3x3 + 3x4
(LP)
s.t. 2x1 4x2 + x3 + 6x4 = 5
x1 + 3x2 + 5x3 2x4 = 7
x1 , x2 , x3 , x4 0.
The optimal objective function value of (LP) is 51
, and the optima
550.361 Optimization, Exam 1, Fall 2012
Problem 1: (25 points) Consider the following simplex tableau. All of the parts for Problem 1
are short answer; you do not need to show any computations at all.
1
2
0
0
0
3
179
1
12
0
1
0
1
0
1
212
1
4
0
1
0
0
1
1
3