Using the network above and the additional information below, find:

$($a$)$ The crash cost per day

$($b$)$ Which activities should be crashed to meet a project deadline of $13$ days at minimum cost. Assume partial crashing is allowed.

$\backslash$table$[[$Activity$,\backslash$table$[[$Crash$],[$Time$],[($days$)]],\backslash$table$[[$Crashed$],[$Cost$],[($total$)]],\backslash$table$[[$Normal$],[$Time$],[($days$)]],\backslash$table$[[$Normal$],[$Cost$]]],[$A$,3,$$$500,4,$$$300$