Suppose that you have an ordered file with $r=40,000$ records stored on a disk with

$[15]$ CO$3$

block size $B=1024$ bytes. File records are of fixed$-$length and are unspanned, with a record size $R=100$ bytes. Now suppose that the ordering key field of the file is $V=11$ bytes long, a block pointer $($block address$)$ is $P=8$ bytes long, and a primary index has been constructed for the file.

Identify the improvement.

b$)$ In case of insertion and deletion in the primary and dense index, which shows higher

$[10]$ CO$3$ overhead? Additionally, which one has more space overhead? Explain the reasons.