  We investigate size Ramsey numbers involving bipartite graphs. It is proved
that, if each forbidden graph is fixed or grows with n (in a certain uniform
manner), then the extremal function has a linear asymptotics.
  The corresponding slope can be obtained as the minimum of a certain mixed
integer program. Applying the Farkas Lemma, we solve the MIP for complete
bipartite graphs, in particular answering a question of Erdos, Faudree,
Rousseau and Schelp (1978) who asked for the asymptotics of the size Ramsey
number of (K_{s,n},K_{s,n}) for fixed s and large n.
