How do I compare multiple rows and get the min of date in a new column?

Question

COMPANY PROD    ID  DATE            NAME        REQD_DATE
XYZ 12345   AAA111  7/1/2011    PETER   
XYZ 12345   PPP222  7/1/2002    JOHN    
MNS 67890   ZZZ999  9/1/2005    STEVE   
MNS 67890   DDD555  9/1/2012    MARTIN  

With reference to this above table say '#temp', Whenever COMPANY AND PROD are same, I want to get the min of date {min(DATE)} into column 'REQD_DATE'

Can someone please help me out here?

Thanks in advance!