Quotable manufactures a removable disk for PC$$s$.$ There are four major stages in its manufacturing. The first stage is coating of disks. Coating is done by an automated machine that can run $24$ hours$/$day$.$ It produces at the rate of $100$ disks$/$hour$.$ The second stage is assembly of the disk into the case. Assembly takes the average worker $2$ minutes$/$disk$.$ There

are $10$ workers at this stage. The third stage is testing, which catches defects from the coating operation. Each testing machine takes $5$ minutes to test a disk. There are $30$ machines and enough operators to keep these machines busy if necessary. The fourth stage is labeling the disk. Each worker here can do $2$ disks$/$minute $($NOT $2$ minutes$/$disk$).$ There are $3$ workers who do this task.

Assume the workforce completes $8$ full hours of work each day, and stages $2$ through $4$ run $8$ hours$/$day$.$ Stage $1$ runs for $24$ hours per day. Demand is $2100$ disks$/$day$.$

Assume all rates and times are deterministic $($no variability in demand or production$).$ Assume $100\%$ quality, that is testing finds no defects.

a$)$ Fill in a table similar to the one below

Stage

Resource

Time $($minutes$/$disk$)$

Capacity for one resource $($disks$/$hour$)$

Capacity for all resources at this stage. $($disks$/$day$)$

$1$

$2$

$3$

$4$

b$)$ Explain why there is sufficient capacity to meet demand.

c$)$ The manager suggests that assembly and labeling can be combined into a single step, so that this single step now has $(10+3)13$ workers. The total raw processing time for one disk does not change. Assume testing is done after this new combined step. Is a reduction in fulltime workforce possible? Show your work.

d$)$ Assume that exactly $10\%$ of the disks from a day$$s production of the coating stage are defective and has to be thrown. Assume testing is done after the new