So for the Max number use the AGGREGATE() Function:
=AGGREGATE(14,6,$C$2:INDEX(C:C,MATCH(1E+99,C:C))/($A$2:INDEX(A:A,MATCH(1E+99,C:C))=I2),1)
Then to find the Capacity a simple SUMIF():
=SUMIFS(B:B,A:A,I2,C:C,K2)

The AGGREGATE() Function was introduced in Excel 2010.
For other versions, the less robust Array Formula MAX(IF()) will work in place of the AGGREGATE:
=MAX(IF($A$2:INDEX(A:A,MATCH(1E+99,C:C))=I2,$C$2:INDEX(C:C,MATCH(1E+99,C:C))))
Being an Array Formula it must be confirmed with Ctrl-Shift-Enter when exiting Edit mode. When done correctly Excel will automatically put {} around the formula to denote an array formula.
Another, If you have the latest Office 365 or using the online app the following non CSE MAXIFS() will work also:
=MAXIFS($C$2:INDEX(C:C,MATCH(1E+99,C:C)),$A$2:INDEX(A:A,MATCH(1E+99,C:C)),I2)
These two are not as robust as the AGGREGATE() in that they will break if there are errors in the data. AGGREGATE() will ignore them.