A function of unknown parameters being estimated from a number of experiments, the problem of optimal (in the sense of minimum variance estimators) design of the experiments is considered. Unlike the papers by Kiefer and Wolfowitz and others, some a priori information about these parameters is assumed to be available. The problem of optimal distribution of measurment time among $n$ fixed experiments is studied. It is proved that there exists the unique solution. For large total measurment time the asymptotic solution is obtained in an explicit form.