Min formula empty cells

Hello, i’ve been trying to find a solution for a few days now, maybe someone here can help me.

I only want to use the min formula, with results the lowest price without the empty cells.
Multiple columns with prices and i want the minium display in a other column without 0.
In Excel it ignore the empty cells or there are other solutions with formulas.
I try something like nested min(if(price1>0,price1))… In Excel can i use array formula.

Would be very grateful for help.