$(13$ pts$)$ An order for $200$ bolts is procesed on work centers $1$ and $2.$ The setup and run times are as follows. It is decided to overlap the lot on the two work centers and to split the lot into two lots. $30$ mlease assume that the transfer lots are found using lot formulation. Move time between operations is $30$ minutes, Work center $2$ cannot be set up until the first lot arrives.

Setup on $A=50$ minutes

Run time on $A=5$ minutes per piece

Setup $onB=100$ minutes Run time $onA=5$ minutes per piece

Run time $onB=7$ minutes per piece

$200$ units $q,$

$q,$Tra

$u$ fer Machine $B$

$($a$)(5)$ Calculate the manufacturing lead time before dverlapping.

b$)(8)$ Calculate the manufacturing lead time after overlapping and saving in manufacturing lead time.

$T_1=\frac{Q_{T}R{T}_A-S{U}_B}{R{T}_A+R{T}_B},T_2=Q_T-T_1$