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We consider an age-structured model of fish population with time-constant fertility and mortality coefficients subject to periodic harvesting. Fishing technology does not allow to harvest fish younger than of a certain age, e.g. because it pases through the net cells. Thus, fishing intensity is age specific with one-dimensional fishing efforts (control). We are to find the algorithm determining the fishing efforts and fishing period providing maximal average profit in the long run. One of the main task is to find the conditions for existence of a time-periodic control showing better performance than constant (steady state) control.