Index: doc/quicktour.dox
===================================================================
--- doc/quicktour.dox	(revision 1514)
+++ doc/quicktour.dox	(revision 1517)
@@ -142,13 +142,23 @@
 Ide Zsuzska fog irni!
 
-<li>Many problems in network optimization can be formalized by means of a
-linear programming problem (LP problem, for short). In our library we decided
-not to write an LP solver, since such packages are available in the commercial
-world just as well as in the open source world, and it is also a difficult
-task to compete these. Instead we decided to develop an interface that makes
-it easier to use these solvers together with LEMON. So far we have an
+<li>Many problems in network optimization can be formalized by means
+of a linear programming problem (LP problem, for short). In our
+library we decided not to write an LP solver, since such packages are
+available in the commercial world just as well as in the open source
+world, and it is also a difficult task to compete these. Instead we
+decided to develop an interface that makes it easier to use these
+solvers together with LEMON. The advantage of this approach is
+twofold. Firstly our C++ interface is more comfortable than the
+solvers' native interface. Secondly, changing the underlying solver in
+a certain software using LEMON's LP interface needs zero effort. So,
+for example, one may try his idea using a free solver, demonstrate its
+usability for a customer and if it works well, but the performance
+should be improved, then one may decide to purchase and use a better
+commercial solver.
+
+So far we have an
 interface for the commercial LP solver software \b CLPLEX (developed by ILOG)
 and for the open source solver \b GLPK (a shorthand for Gnu Linear Programming
-Toolkit). 
+Toolkit).
 
 We will show two examples, the first one shows how simple it is to formalize
@@ -158,5 +168,5 @@
 <ol>
 <li>The following code shows how to solve an LP problem using the LEMON lp
-interface. 
+interface. The code together with the comments is self-explanatory.
 
 \code
@@ -205,6 +215,60 @@
 See the whole code in \ref lp_demo.cc.
 
-<li>The second example shows how easy it is to formalize a network
-optimization problem as an LP problem using the LEMON LP interface.
+<li>The second example shows how easy it is to formalize a max-flow
+problem as an LP problem using the LEMON LP interface: we are looking
+for a real valued function defined on the edges of the digraph
+satisfying the nonnegativity-, the capacity constraints and the
+flow-conservation constraints and giving the largest flow value
+between to designated nodes.
+
+In the following code we suppose that we already have the graph \c g,
+the capacity map \c cap, the source node \c s and the target node \c t
+in the memory. We will also omit the typedefs.
+
+\code
+  //Define a map on the edges for the variables of the LP problem
+  typename G::template EdgeMap<LpDefault::Col> x(g);
+  lp.addColSet(x);
+  
+  //Nonnegativity and capacity constraints
+  for(EdgeIt e(g);e!=INVALID;++e) {
+    lp.colUpperBound(x[e],cap[e]);
+    lp.colLowerBound(x[e],0);
+  }
+
+
+  //Flow conservation constraints for the nodes (except for 's' and 't')
+  for(NodeIt n(g);n!=INVALID;++n) if(n!=s&&n!=t) {
+    LpDefault::Expr ex;
+    for(InEdgeIt  e(g,n);e!=INVALID;++e) ex+=x[e];
+    for(OutEdgeIt e(g,n);e!=INVALID;++e) ex-=x[e];
+    lp.addRow(ex==0);
+  }
+  
+  //Objective function: the flow value entering 't'
+  {
+    LpDefault::Expr ex;
+    for(InEdgeIt  e(g,t);e!=INVALID;++e) ex+=x[e];
+    for(OutEdgeIt e(g,t);e!=INVALID;++e) ex-=x[e];
+    lp.setObj(ex);
+  }
+
+  //Maximization
+  lp.max();
+
+  //Solve with the underlying solver
+  lp.solve();
+
+\endcode
+
+The complete program can be found in file \ref lp_maxflow_demo.cc. After compiling run it in the form:
+
+<tt>./lp_maxflow_demo < ?????????.lgf</tt>
+
+where ?????????.lgf is a file in the lemon format containing a maxflow instance (designated "source", "target" nodes and "capacity" map).
+
+
+See the whole code in \ref lp_demo.cc.
+
 
 </ol>
