Well, you can do this with a formula but it's not very scalable. For example, you can do this:
=SUM(MIN(A1:B1),MIN(A2:B2),MIN(A3:B3), MIN(A4:B4))
that will work in the case you described. However, I appreciate that if you have a large number of rows then this won't scale nicely. In that case, I think you'll need a VBA macro as I can't see a way to do this. I'm prepared to be corrected though by some Excel formula guru.
For a VBA solution, you can try the following (found in the OzGrid forums):
Function sumOfMax(ByVal inputRange As Range, Optional doMin As Boolean) As Double
Dim inRRay As Variant
Dim currentMax As Double
Dim i As Long, j As Long
Set inputRange = Application.Intersect(inputRange, inputRange.Parent.UsedRange)
If Nothing Is inputRange Then Exit Function
inRRay = inputRange.Value
For i = 1 To UBound(inRRay, 1)
currentMax = Val(inRRay(i, 1))
For j = 1 To UBound(inRRay, 2)
If (Val(inRRay(i, j)) > currentMax) Xor doMin Then currentMax = Val(inRRay(i, j))
Next j
sumOfMax = sumOfMax + currentMax
Next i
End Function
When set to TRUE
, the optional parameter calculates the minimums as opposed to the maximums that this macro calculates by default. In your example, you would need to call it like this:
=sumOfMax(A1:B4, TRUE)
Just remember you need to place the code in a standard code module.