Anguilla Manufacturing is interested in using the data collected during value stream mapping to evaluate the current state performance of the capacity of its manual assembly line process under different batch size assump$-$tions. The availability of processing per shift, after accounting for breaks and a mid$-$shift employee meeting, is $436$ minutes. The current operating characteristics of each processing step are found in the accompanying table. Note that each step can process only one part at a time and all steps must process the same sized batches. Saw

Cycle time per part

Setup time per batch

Sand Drill Assemble Mark $20$ seconds $15$ seconds $30$ seconds $25$ seconds $10$ seconds $3$ minutes $4$ minutes $0$ minutes $3$ minutes $8$ minutes

a$.$ Calculate the average processing time per unit and the capacity at each step assuming batch sizes of: i$.10$ units

ii$.20$ units iii. $30$ units iv$.40$ units

b$.$ Identify the bottleneck operation and the line$$s pro$-$cessing capacity for each batch size listed in part $($a$).$

c$.$ Explain why batch sizes beyond $40$ units will not increase the line$$s processing capacity further.