Practice question $($with Rework$)$ July $2024$

A confectionary constitutes three operations $($A$,$ B and C$)$ as illustrated in the figure below.

Inspection is performed at each stage. In order to recover poorly mixed dough, a rework

station D is set up after station B$.$ The scrap rates for operation A$,$ B$,$ C & D are as follows:

d$\_$A$=5\%,$ d$\_$B$=3\%,$ d$\_$C$=7\%,$ and d$\_$D$=40\%.$

Determine the number of units at each operation that the bakery manager must process in order to meet the required output of $100000$ loaves per day.