Basis information in GAMS

> How do I found out which variables and slacks are basic and non-basic.

Look at the marginals.  Nonzero or EPS marginals means non-basic and zero marginals means basic. In GAMS marginals are duals for the rows and reduced costs for the columns. Of course row duals can be interpreted as reduced costs for the corresponding slacks. For instance when looking at the solution from the trnsport model we see:

                           LOWER          LEVEL          UPPER         MARGINAL
 
---- EQU cost                .              .              .             1.0000 Non-basic   
  
---- EQU supply  observe supply limit at plant i
 
                 LOWER          LEVEL          UPPER         MARGINAL
 
seattle          -INF          350.0000       350.0000         EPS Non-basic        
san-diego        -INF          550.0000       600.0000          .  Basic        
 
---- EQU demand  satisfy demand at market j
 
                LOWER          LEVEL          UPPER         MARGINAL
 
new-york       325.0000       325.0000        +INF            0.2250 Non-basic     
chicago        300.0000       300.0000        +INF            0.1530 Non-basic     
topeka         275.0000       275.0000        +INF            0.1260 Non-basic     
 
---- VAR x  shipment quantities in cases
 
                          LOWER          LEVEL          UPPER         MARGINAL
 
seattle  .new-york          .            50.0000        +INF             .     Basic     
seattle  .chicago           .           300.0000        +INF             .     Basic     
seattle  .topeka            .              .            +INF            0.0360 Non-basic     
san-diego.new-york          .           275.0000        +INF             .     Basic     
san-diego.chicago           .              .            +INF            0.0090 Non-basic     
san-diego.topeka            .           275.0000        +INF             .     Basic     
 
                           LOWER          LEVEL          UPPER         MARGINAL
 
---- VAR z                 -INF          153.6750        +INF             .    Basic      
 
 

This model has 6 equations and 7 variables. So we expect 6 basic rows/columns and 7 non-basic ones. This indeed is the case.

Note: this model is dual degenerate as it has an EPS marginal. This means the dual of equation supply('seattle') is numerically zero but non-basic nevertheless. This indicates presence of alternative optimal solutions.