An agregate plan is being developed for the next three periods using the transportation method of aggregate pl$-$anning. You start the period with $500$ units in inventory. Other necessary information rovided in the table below. You need to schedule for any overtime to be worked before the aggregate planning period begins. How much overtime is to be worked in each of the three periods $(1,2,$ and $3,$ respectively$)$ if you follow the lowest cost plan?

$\backslash$table$[[$Period$,\backslash$table$[[$Units$],[$needed$]],\backslash$table$[[$Regular$],[$Time$]],\backslash$table$[[$Over$],[$time$]],\backslash$table$[[$Sub$-],[$contract$]],\backslash$table$[[$Initial$],[$inventory$],[$Regular time$],[$cost$]],\backslash$table$[[500$ units$],[$$$\frac{50}{?}$ unit$]]],[1,2000,2000,550,1000,$Overtime cost,$$\frac{60}{?}$ unit$],[2,2000,2000,$$$00,1000,\backslash$table$[[$Subcontracting$],[$cost$]],$$$\frac{70}{?}$ unit$]]$