This preprint was accepted December 26, 2005
ABSTRACT: We are going to give a formula for the exact Bellman function of a certain ``toy'' two weight problem. This adds one more function to a short list of other Bellman functions for which the precise formulae were found recently. Our case study reveals essential features of finding Bellman functions in general. It gives the extremal sequences for the problem. We also ask some open questions.[Full text: (.ps.gz)]