4.5 Sensitivity or Postoptimality Analysis 217SinceA 1 is changed, we have
c 1 =c 1 −πTA 1 = − 45 −(−^223 −^23 ){
6
10
}
=^173
Asc 1 is positive, the original optimum solution remains optimum for the new problem
also.
Example 4.10 Find the effect of changingA 1 from
{ 7
3}
to{ 5
6}
in Example 4.5.SOLUTION The relative cost coefficient of the nonbasic variablex 1 for the newA 1
is given by
c 1 =c 1 −πTA 1 = − 45 −(−^223 −^23 ){
5
6
}
=−^133
Sincec 1 is negative,x 1 can be brought into the basis to reduce the objective function
further.For this we start with the original optimum tableau with the new values ofA 1
given by
A 1 =B−^1 A 1 =
[ 4
15 −
1
15
− 1501 752] {
5
6
}
=
[ 20
15 −
6
15
− 301 + 254]
=
{ 14
15
19
150}
VariablesBasic variables x 1 x 2 x 3 x 4 x 5 x 6 −f bi (bi/ais)
x 3 1415 0 1 73 154 − 151 0 8003 400014
x 2 15019 1 0 − 301 − 1501 752 0 403 200019 ←
Pivot element
−f −^1330050322323128 , 3000
↑x 3 0 −^1401914919196 − 195 0 3 , 19200
x 1 1 15019 0 − 195 − 191 194 0 2 , 19000
−f 0 65019 0 29519 13519 3019 1 18619 ,^000Since allcjare nonnegative, the present tableau gives the new optimum solution as
x 1 = 0002 / 19 , x 3 = 2003 / 19 (basic variables)
x 2 =x 4 =x 5 =x 6 = 0 (nonbasic variables)fmin= −186 , 000
19
and maximum profit=