Possible Sumproduct or similar issues

Hi - before I start thanks for looking and also thanks for any advice you may be able to give.

My company has a weighbridge which records dates, times, product codes, weight etc. I would like to sum the tonnages of INcoming Products on certain dates but I'm unsure how to add criteria within formulas - possibly the Match function?

On the attached spreadsheet I would like cell B2 to show the sum of AUP01 brought INto the site on 15/05/13. It should read 6 (J1+J8)

Thanks again...