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11-20-2017 11:58 AM

If we have this problem (you can see it in https://www.slideshare.net/orajjournal/a-single-stage-single-constraints-linear-fractional-programmi...), can we solve with SAS?

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Posted in reply to dali74

11-20-2017 12:30 PM

There are a number ways. Take a look at: https://blogs.sas.com/content/iml/2016/12/19/solve-linear-programming-problems-sas.html

Art, CEO, AnalystFinder.com

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Posted in reply to dali74

11-20-2017 12:40 PM

Here are three ways:

```
/* linear fractional programming problem (NLP) */
proc optmodel;
var x {1..2} >= 0;
max z = (x[1] + 3) / (x[2] + 1);
con c1: -x[1] + x[2] <= 1;
con c2: 2*x[1] <= 3;
con c3: 3*x[1] + 2*x[2] <= 7;
solve;
print x;
quit;
/* linear programming transformation from Das/Mandal paper (LP) */
proc optmodel;
var y {1..2} >= 0;
max z = y[1] - y[2] + 3;
con c1: -y[1] + 2*y[2] <= 1;
con c2: 2*y[1] <= 3;
con c3: 3*y[1] + 9*y[2] <= 7;
solve;
print y;
quit;
/* linear programming problem from Charnes/Cooper transformation (LP) */
/* https://en.wikipedia.org/wiki/Linear-fractional_programming#Transformation_to_a_linear_program */
proc optmodel;
var y {1..2} >= 0;
var t >= 0;
max z = y[1] + 3*t;
con c1: -y[1] + y[2] <= t;
con c2: 2*y[1] <= 3*t;
con c3: 3*y[1] + 2*y[2] <= 7*t;
con c4: y[2] + t = 1;
solve;
print y;
impvar x {j in 1..2} = y[j].sol / t.sol;
print x;
quit;
```

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Posted in reply to dali74

11-21-2017 08:34 AM

SAS/IML also can do that . If you want IML solution, post it at IML forum. Rick is there.