$($c$)$ Assume that only $12$ memory blocks are available. By considering the cost of disk block

transfers only, suggest the best evaluation plan for the query. Particularly, you need to do the

followings.

i$.$ Transform the unoptimized relational$-$algebra expression in $($a$)$ into an equivalent

optimized expression for producing your suggested evaluation plan. Show all the steps and

state clearly the rule number of the equivalence rule you used in each step.

ii$.$ Draw the fully annotated evaluation plan, including exactly what algorithms and index, if

any, are used for each operation and how the execution of the operations is coordinated

$($materialization or pipelining$).$

iii. Indicate in the evaluation plan the memory allocation $($number of memory blocks allocated

to each input, output $($b

b

$),$ but the total cannot exceed the available memory at one time$).$

iv$.$ Find the cost of each operation and the total cost of the whole plan in number of disk

block transfers.

v$.$ State clearly any justifiable assumptions you have made in your estimation