…
for 5 shoes of 1st type and 6 types of 2nd Type.
Maximize
{Z = x1 + x2 + x3 }
Subject to:
2 x1 + 5 x2 + 4 x3  130 & 3 x1 + 6 x2 + 2 x3  150
&
x1, x2, x3, x4  0
1. Converting the inequalities to equalities using the slack variables.
2 x1 + 5 x2 + 4 x3 + x4 = 130
3 x1 + 6 x2 + 2 x3 + x5 = 150
2. Constructing the Simplex Tables one has:
xx1 1
A
x2
x3
A
x5
x2
1
x3
x4
22
5
4
13065
x4
-2/3
x5
33
2
2
6
2
15050
150
x1
1/3
2
2/3
5075
Z
-1
-1
-1
-1
Z
1/3
1
-1/3
50
Any (-1) can be considered to
determine the pivot column.
But we will choose the first (Why?)
x3
0
x5
x2
0.25
0.375
x4
0.375
11.25
-0.25
42.5
0.125
53.75
x1
Z
0.25
1.125
Since all the elements of the last row are all positive
Therefore:
The optimum solution is reached.
Hence:
x1 = 42.5
&
x2 = 0
&
x3 = 11.25
And:
Z=
42.50
8/3
8/3 3050
SAME
VALUE
+ 0 + 11.25
= 53.75
Which is the required Max.
OR Illustrative Examples - Ragab 1434
Good
01
Luck
Dr. Eng. Moustafa Reda AbdALLAH