R linear programming set up in linprog package ignores constraint (less than or equal to) using solveLP

Question

I am using solveLP in the linprog R package to solve a simple linear programming problem:

minimize -x1-x2 
subject to 2*x1+x2+x3    =12
           x1+2*x2   +x4 = 9
           x1,x2,x3,x4 >=0

which has dual equivalent:

maximize 12*y1+9*y2 
subject to 2*y1+y2 <= -1
           y1+2*y2 <= -1
           y1,y2 <=0

If I state the problem in the primal form I get the right results (5,2,0,0). But when stating the problem in the dual form, the first two constraints simply get ignored. I get the result (0,0) which clearly violates (2*y1+y2 <= -1 and y1+2*y2 <= -1), is there an extra setting or parameter I am missing ? Please have a look at the code underneath and let me know what you think:

require(linprog)
objVec <- c(-1,-1,0,0) 
rhsConstr <- c(12, 9,0,0,0,0) 
Amat <- rbind( c( 2, 1, 1, 0 ),
               c( 1, 2, 0, 1 ),
               c( 1, 0, 0, 0 ),
               c( 0, 1, 0, 0 ),
               c( 0, 0, 1, 0 ),
               c( 0, 0, 0, 1 ))
res <- solveLP( objVec, rhsConstr, Amat, maximum=FALSE, const.dir = c("==","==",">=",">=",">=",">=") , lpSolve=TRUE)
res$solution

# dual problem - this is where the problem is
objVec <- c(12,9) 
rhsConstr <- c(-1.0,-1.0,0,0) 
Amat <- rbind( c( 2, 1),
               c( 1, 2), 
               c( 1, 0),
               c( 0, 1))
res <- solveLP( objVec, rhsConstr, Amat, maximum=TRUE, const.dir = rep("<=",length(rhsConstr)))
res$solution

In positive space the dual problem does give the right answer (1/3,1/3):

objVec <- c(12,9); 
rhsConstr <- c(1,1,0,0); 
Amat <- rbind( c( 2, 1), c( 1, 2), c( 1, 0), c( 0, 1)); 
res <- solveLP( objVec, rhsConstr, Amat, maximum=FALSE, const.dir = rep(">=",length(rhsConstr)) , lpSolve=TRUE); 
res$solution; 

Answer 1

As with many linear programming libraries, there are implicit non-negative constraints, y>=0: there are no feasible solutions (but I would expect res$status to indicate this).

solveLP does not seem to allow negative solutions: you can either transform the problem to have only non-negative values (replace y1 with u1-v1, y2 with u2-v2) or use another package, that allows negative values.

library(Rglpk)
objVec <- c(12,9) 
rhsConstr <- c(-1.0,-1.0,0,0) 
Amat <- rbind( c( 2, 1),
               c( 1, 2), 
               c( 1, 0),
               c( 0, 1))
Rglpk_solve_LP( 
  objVec, Amat, rep("<=",4), rhsConstr,
  bounds = list( lower = list( ind=c(1L,2L), val=c(-Inf,-Inf) ),
                 upper = list( ind=c(1L,2L), val=c( Inf, Inf) ) ), 
  max=TRUE
)