EM602
I
CM710
(NJ)
Management Science
Lecture 5
Sensitivity Analysis
Homework Problem
#3
(Solve
by MTechnique)
Consider the following linear program:
Minuiilze
2
=
8Os,
+60.r1
subject to
O.ZO.K,
+0.32.r2
5
0.25
I,
+
.K, =
1
.K,
.
S.
2
0
Assignments from Lecture 4
l
Handout Problem
#3
(solve probkm by
both MTechnique and TwoPhase
Technique)
l
Problems
35,
322(a), 322(d)
l
Read Sections
353.6
Homework Problem
#3
(Step Ml
6
M2

Modify
6
Add Artiftcials)
The constraints in standard form
become:
Minimize
2
=
801,
+60x2
subject to
.20x,+.31x,
+s,
=3
(slack
IS
added)
_K,
+x1
+R,
=
1
(Artificial is added)
I,
..‘I,
3,
.
R,
2
0
Homework Problem
#3
Homework Problem
#3
(Step
M3,
M4,
MS

Modify Obj Function)
(Step M6

Starting Simplex Solution)
Augment the Objective Function to
include the Arttfkial Variable, penalize
it, then
sdve
for and
condition
it to
remove the
artiftcial
variable
Minimize
z
=
8O.r,
+6&r,
IS
augmented to
z
=
8t)s,
+
6o.r, +
R,
and
penalized to become
z
=
~OS,
+6&K:
+
JR,
z

~O.K,

60.~~

.\I(
I

.‘c,

x2
)
=
0
~+(80+.\/)_K~
+(a+.\/)~:
=
.\f
The Basic Feasible Solution for the
problem
with
4 variables and 2
equations can now be written:
s,
= 0.25
R, =
I
.K,_.K.
=
0
,?=
.\I
The problem can then be solved by the
simplex method
EM602
/
QM710 (NJ)
Lecture
5’
Page 5l