First of all, the header of the mapping table data set needs to be adjusted. Unmerge those cells that are merged and then give each column a title. Doing so should result in something similar to this:

I then created a results table on a second worksheet that looks like this:

It may be grossly over-simplified, but hopefully you can modify the formula as needed.
Now here's the formula I created in C2:
{=INDEX(MappingTable!$K$1:$S$1,1,SUMPRODUCT(IF(B2<INDIRECT("MappingTable!"&ADDRESS(MATCH($A2,MappingTable!$I$2:$I$15,0)+1,11)&":"&ADDRESS(MATCH($A2,MappingTable!$I$2:$I$15,0)+1,19)),1,0))+1)}
Note: This is an array formula and must be committed with Ctrl+Shift+Enter. The curly braces - { } - that surround the formula above will not be entered by the user, but will be created once the formula is committed as described above.
KEY NOTES:
B2 will reference the Contract Value in your results table.
"MappingTable!" is a hardcoded value that should be the name of your sheet plus the exclamation point at the end.
$A2 will reference the Case Type in your results table.
MappingTable!$I$2:$I$15 is an absolute reference to the row headers on the mapping table.
11, which is found in the first ADDRESS function, is a reference to Column K on the mapping table worksheet. It can also be written as COLUMN(K:K).
19, which is found in the secondADDRESS function, is a reference to Column S on the mapping table worksheet. It can also be written as COLUMN(S:S).