Help with sumifs and only certain numbers

[BCP]

2010 Excel

Not sure if sumif is the correct function here, but I will attempt to explain what I want to do.

I'm creating a chart that looks something like the below:


Roof Carport Ground
MA 11 14 18
NJ 8 8 18
PA 6 6 18
DE 7 7 18
MD 6 6 18
DC 7 7 18


below the data I have 3 columns. Column 'A' has a number, column 'B' either one of the options on the 'x' and 'y' axis of the chart (roof, carport, MA, NJ, etc), and Column 'C' of 4 options not shown on the chart (Criteria 1, Critera 2...etc). I currently have used the sumif functions to add up all the numbers in column 'A' where column 'B' matches the appropriate x and y axis designators.

However, when the B and C columns match up, I only want to count the larger of the two numbers in the first column (so for instance when I have something like this:

2 MA criteria 1
5 MA criteria 2
4 MA criteria 1

I want all 'MA' cells in the chart to count rows 2 and 3 (and ignore row 1 since column 'A' is lower in row 1 than row 4 - rows 1 and 3 are only compared in this respect because column 'C' matches).

I hope I've explained this correctly and thanks for any help that can be offered.