Help on Conditional Min Function

Thanks sandiptemkar and Fdibbins.

Can you elaborate more on the formula? I want to set up a conditional Min function that can automatically run when the item changes.Here you already have the Min value for each item,thus you can run Pivot. But what I need is the Min formula that can automatically fill in the Min clumn.
Attached is the file for your ref. I want to fill in column Min but the list is too long for copying and pasting formula item by item.

Thank you for your kind help !