We discuss a model of a leaky quantum wire and a family of quantum dots described by Laplacian in L<sup>2</sup>(<sup>2</sup>) with an attractive singular perturbation supported by a line and a finite number of points. The discrete spectrum is shown to be nonempty, and furthermore, the resonance problem can be explicitly solved in this setting; by Birman-Schwinger method it is reformulated into a Friedrichs-type model.