The manager of the State University's DED computer wants to be able to access five different files. These files are scattered on ten disks as shown in table below. The amount of storage required by each disk is as follows: disk1, 3K; disk2, 5K; disk3, 1K; disk4, 2K; disk5, 1K; disk6, 4K; disk7, 3k; disk8, 1K; disk9, 2K; disk10, 2K.

a) Formulate an IP that determine a set of disks requiring the minimum amount of storage such that each file is on at least one of the disks. For a given disk, we must either store the entire disk or store none of the disk; we cannot store part of a disk

b) Modify your formulation so that if disk 3 or disk 5 is used, then disk 2 must also be used.

Disk

1 2 3 4 5 6 7 8 9 10

File 1 X X X X X X
File 2 X X
File 3 X X X X
File 4 X X X
File 5 X X X X X X X