We consider functions which are the sum of theklargest order statistics in a sample of sizenfrom a continuous distributionF, minusnh, wherehis a specified constant. We prove that such functions are concave inn. IfFis an exponential distribution, then for a fixedkwe obtain that value ofnwhich maximizes the expected value of the function defined above. ForFIFR we obtain an upper bound onnand also an upper bound on the maximum of the expected value of the function.