14 The manager of State University’s DED computer wants to be able to access five different files. These files are scattered on 10 disks as shown in Table 13. The amount of storage required by each disk is as follows: disk 1, 3K; disk 2, 5K; disk 3, 1K; disk 4, 2K; disk 5, 1K; disk 6, 4K; disk 7, 3K; disk 8, 1K; disk 9, 2K; disk 10, 2K.

a Formulate an IP that determines 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.

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TABLE 12 Glue Production Line 1 2 3 1 2 20 50 20 355 45 45 30 40