Let’s assume the farmers goals are: Costs $15000, revenues $60000 and N contamination 300 units. All these goals can be overachieved (with individually defined weights) or underachieved (with individually defined weights). On following Excel sheet both normalized an original weights are included, but the model is solved only with the normalized ones.
Solving these linear programming model using Linkosa
software our manager obtains following optimal solution:
Optimal Solution of the Model FARM PRODUCTION Goal Programming Approach B  
Min. value of the objective function Z (norm weights)  
31,27


Structural variables  Constraints  
Name  Value  Type  Name  Value  Slack  
wheat [ha] 
8

Basic  arable land 
30

0


barley [ha] 
0

Lower bound  acreage of wheat 
8

0


potato [ha] 
22

Basic  acreage of potato 
10

12


grassland [ha] 
3,97

Basic  acreage of grassland 
15

11,03


cows [pcs] 
4,52

Basic  balance of food 
0

0


milk [l] 
18,08

Basic  stable capacity 
30

25,48


u1 
0

Lower bound  balance of milk 
0

0


u2 
0

Lower bound  costs 
150

0


u3 
0

Lower bound  revenues 
600

0


e1 
81,05

Basic  N contamination 
300

0


e2 
0

Lower bound  
e3 
146,8

Basic 