The main aim of the paper is to determine the extreme values of the product P=a_1a_2\cdots a_n under the constraints \sum_{i=1}^n a_i=S and \sum_{i=1}^{n}\frac 1{a_i+1}=S_0 for n\ge 3 nonnegative real numbers a_1,a_2,\ldots, a_n and some given constants S and S_0. Some interesting applications of our results are provided as well.



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 Cîrtoaje, Vasile, Giugiuc, Leonard