Problem $2$: ITSD is attempting to backup data on some external harddrives and have asked you

for help. The data files have sizes $240,462,117,560,379,110,341,294,503,469,90,65,617,500,$

$550,$ and $400$ GB $.$

a$)$ If the capacity of a harddrive is $780$ GB $,$ write a concrete integer programming model to

determine the minimum number of harddrives needed to backup all files. Hint: You need two

types of variables: one of which tells you which file is assigned to a hard drive and one of

which tells you if a hard drive is used. Make sure you include logical constraints to relate these

variables.

b$)$ Convert your concrete model to a parameterized model.

c$)$ How many total variables does your model have?