f$.$ What is the new value stream's processing time?

$13.$ 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 assumptions. 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.

$\backslash$table$[[,$Saw,Sand,Drill,Assemble,Mark$],[\backslash$table$[[$Cycle time$],[$per part$]],20$ seconds,$15$ seconds,$30$ seconds,$25$ seconds,$10$ seconds$],[\backslash$table$[[$Setup time$],[$per batch$]],3$ 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 processing 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.