128 Optimization: Algorithms and Applications
The following constraints are specied on the investment.
• No more than $140,000 in the transport segment
• No more than $160,000 in the computer segment
• No more than $120,000 in the appliances segment
• No more than $230,000 in the German segment
• No more than $220,000 in the USA segment
The LPP can be written mathematically as
Maximize
z = 0.095x
1
+ 0.112x
2
+ 0.105x
3
+ 0.119x
4
+ 0.117x
5
+ 0.132x
6
+ 0.105x
7
+0.109x
8
+0.055x
9
+ 0.051x
10
subject to
x
1
+ x
2
≤ 140
x
3
+ x
4
≤ 160
x
5
+ x
6
≤ 120
x
1
+ x
7
≤ 230
x
3
+ x
4
+ x
8
≤ 220
x
1
+ x
2
+ x
3
+ x
4
+ x
5
+ x
6
+ x
7
+ x
8
+ x
9
+ x
10
= 600
x
1
, x
2
, x
3
, x
4
, x
5
, x
6
, x
7
, x
8
, x
91
, x
10
≥ 0
Writing the problem in standard form
Minimize
z = −0.095x
1
− 0.1