filtering and removing the rest except all the smallest available, please help!

I want to ask if there’s any way to help remove those highlight in red by any function with the following criteria.

When the period (i.e. date 1 and 2) are the same,
- Keep the cheapest available (if price is 0, it means unavailable)
- Keep all cheapest even when their price are the same

date 1 date 2 supplier price
01-Jul 02-Jul A US$16
01-Jul 03-Jul A 0
01-Jul 03-Jul B US$22
02-Jul 03-Jul A US$15
02-Jul 03-Jul B US$15
02-Jul 03-Jul C US$18