# 101879095-Class-13 by sakinajhatial

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• pg 1
```									           Post optimal or Sensitivity Analysis

1. Changes affecting feasibility
Ø  Feasibility of simplex solution is affected in one of the
two ways.

üan increase or decrease in the resource (change in
right hand side)

A new constraint is added in the model
ü

8/2/12                                   1
1
Change in resource

Let total glazing time by the company is reduced from 1499 to
400 hours. Find the maximum revenue.

Basic x1
Optimum Tableaux2     s1   s2    s3    s4     b

Z     0     0    0  20/      0   32/3 1266
3                 0
s1     0     0    1 -2/3      0   -5/3 84

x1     1     0    0    1/3    0   -2/3 333
s1    1 -2/3 0 -5/3                1500    2450/3
s3   0    0    0 -1/3          1 -1/3 17
x1    0 1/3 0 -2/3                  400 =  -100/3
s3    0 negative and
x1 becomes-1/3 1 0 -1/3 z         16000/3 1150/3
600
8/2/12                                          2
x2   0    1        0          =0    1 250                   2
Dual Simplex
Basic   x1 x2 s1       s2      s3    s4    b

z    0     0    0  20/      0    32/3 16000
3                  /3
s1    0     0    1 -2/3      0    -5/3 2450 /
3

x1     1  0  0 1/3          0 -2/3 -100 /
Basic   x1 x2 s1 s2          s3 s4     b
3
s3     0  0       0   -1/3 1 -1/3 1150 /
z    16 0       0     12 0    0   4800         Optim
3
s1 -5/2 0        1    -3/2 0   0    900         um
x2     0  1       0     0   0  1    250
Tablea
Ratio z/x1                      16 Min.
u
s4    -3/2 0      0
8/2/12-1/2   0     1     50         3
3
If the available hours for polishing is 800, then

8/2/12                               4
4
From above tableau,

x1 = 333- 1/3 s2 + 2/3 s4 &     x2 = 250- s4

Put the values of x1 and x2 in new constraint; i.e. x1 + 2x2 + s5 =
800

we will get

-1/3 s2 -4/3 s4 + s5 = -33
8/2/12                                    5
5
Using     dual
simplex

8/2/12   6
6
8/2/12   7
7
Post optimal or Sensitivity Analysis

2. Changes affecting Optimality
Ø  Optimality of simplex solution is affected in one of the
two ways.

A change in objective function
ü

ü

8/2/12                                    8
8
Change in objective function

Suppose plain tiles is sold for Rs. 40 instead of Rs. 20. The
objective function will become:

Z = 40x1 + 24x2

y1 , y2 , y3 , y4 =

1 -2/3 0               -5/3
0 , 40 , 0 , 24 0 1/3 0                 -2/3 = 0,40/3,0,-8/3
0 -1/3 1               -1/3
Basic x1 x2 s10 s20
0                      s3 s4
1        b

Z      0     0       0    20/   0   32/3 1266
3              0
Y1    s1      0     0       1 -2/3
8/2/12      0   -5/3 84              9
9
Find Optimum Tableau
Basic   x1 x2 s1         s2   s3   s4     b

z     0   0    0  40/       0    -8/3 12660
3
s1    0   0    1 -2/3       0    -5/3   84

x1     1  0  0 1/3           0 -2/3      333
Basic   x1 x2 s1 s2           s3 s4        b

s3    0   0   0 -1/3 1 -1/3 17
z    0   8/3 0 40/ 0    0 39980/
3          3
x2    0   1   0  0   0  1   250
s1    0   5/3 1 -2/3 0   0 1502/3

8/2/12              Non optimal solution
10
10
8/2/12   11
11

8/2/12   12
12
1   -2/3   0   -5/3     1 1/3
x3 constraint column= 0    1/3   0    -2/3      1 =   1/3
0   -1/3   1   -1/3     2     5/3
0    0     0       1     00
Basic x1 x2 x3 s1 s2 s3                s4     b

Z     0    0    -   0 20/ 0 32/3 1266
10/3    3          0

s1     0    0   1/3    1 -2/3 0 -5/3 84
Basic x1 x2 x3 s1 s2 s3                s4     b
x1     1    0 1/3   0 1/3 0 -2/3 333
Z     0    0  0     0 6 2 46/9 1269
4
s3     0    0 5/3 0 -1/3 1 -1/3 17
s1     0    0  0     1 -3/5 -1/5 - 403/
8/2/12          10/9 5                   13
13

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