Avoid Duplicate Records

In the attached Sheet if there is any repeated name I can select the unique records by pulling up the formula (=IF(COUNTIF(C$1:C2,C2)=1,MAX(A$1:A1)+1,"") in column A pulling it up to get the serial number , and delete the blank records by selecting blanks through Auto Filter. The Challenge is I want have only those unique records which have the minimum amount, as final output given in sheet 2. Every time i get a new piece of data which contains some of the old entries (Name) with reduced amount and some of the new entries, i want keep the old entries (Name) with reduced amount and new entries (Name) with new amount. Please help , Thanks in advance.