A Research and Development team is creating a project plan for developing a new product. Upper management has requested the project be completed in $52$ days. They have developed estimated time durations in days for the project as shown in the following table.

$\backslash$table$[[$Activity$,$Immediate Predecessor Activities,Optimistic Time $($t$\_(0)),$Most Likely Time $($t$\_($m$)),$Pessimistic Time $($t$\_($p$))],[$A$,,8,10,13],[$B$,$A$,4,8,12],[$C$,$A$,8,13,18],[$D$,$A$,7,7,16],[$E$,$B$,3,4,6],[$F$,$C$,$E$,8,10,11],[$G$,$B$,10,12,14],[$H$,$B$,$D$,16,19,22],[$I$,$B$,$D$,8,13,18],[$J$,$F$,$G$,$H$,6,8,12]]$

Determine the estimated duration of the project.

$38$ days

$46$ days

$52$ days

$67$ days