44
Chapter 4
Linear Programming: The Simplex Algorithm
4.10
(continued)
Solution:
X = 200 square feet, Y = 800 square feet, S
3
= 400 square
feet, S
4
= 400 square feet.
Meaning:
Devote 200 square feet to decorations and 800 square feet to
toys.
S
3
is the amount by which the minimum toy space is exceeded and
S
4
is the amount by which the space devoted to toys exceeds twice that
devoted to decorations.
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Solutions Manual and Workbook
45
4.11 MAX Z:
2X
1
+ 3X
2
+ 5X
3
Subject to:
X
1
+
X
2
+
X
3
= 10
X
1
–
X
3
≥
4
X
2
≤
3
(X
1
, X
2
, X
3
≥
0)
Tableau 1
X 1 X 2 X 3 A1 S2 A2 S3
Cj
2 3 5 
M
0 
M
0
Bi
Θ
A1

M
1 1 1 1 0 0 0 10 10
A2

M
1 0 1 0 1 1 0
4 4
S3
0 0 1 0 0 0 0 1
3 +
∞
Zj
2
M

M
0 
M M

M
0 14
M
∆
Zj
2+2
M
3+
M
5 0 
M
0 0
Entering:
X 1
Leaving:
Artificial 2
Optimal Tableau
X 1 X 2 X 3
A1
S2
A2 S3
Cj
2
3
5

M
0

M
0
Bi
X 3
5 0 0.50 1 0.50 0.50 0.50 0 3
X 1
2 1 0.50 0 0.50 0.50 0.50 0 7
S3
0 0
1
0
0
0
0 1 3
Zj
2 3.50 5 3.50 1.50 1.50 0 29
∆
Zj
0 0.50 0 3.5
M
1.50 1.5
M
0
Solution:
X
1
= 7,000 acres, X
3
= 3,000 acres, S
3
= 3,000 acres.
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 Spring '10
 Koslov
 Linear Programming, Zagreb, square feet, Simplex algorithm

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