Sequential design in an Urn model

Finitely many urns are filled with balls each having one of the labels 1,.Nin known proportions. Balls can be drawn with replacement from any urn at the cost of c>0 monetary units per drawing. Let X ₄be the number of labels that show up in the first kdrawings. We solve the problem to find a selection rule for the urns to be used and a stopping rule such that E(X _τ–eτ) is maximized. A second problem of this kind is also treated.