Consider a line that makes two different astronomical digital cameras. The TS$-7$ costs

Consider a line that makes two different astronomical digital cameras. The TS$-7$ costs

$$2,000$ while the TS$-8,$ which uses a much larger chip, costs $$7,000.$ Most of the cost of the

$$2,000$ while the TS$-8,$ which uses a much larger chip, costs $$7,000.$ Most of the cost of the

cameras is due to the cost of the chip. In manufacturing, both go through the same three

cameras is due to the cost of the chip.

steps but take different amounts of time. The capacities for the TS$-7$ are seven, five, and six

per day at workstations $1,2,$ and $3,$ respectively $($that is$,$ if we run exclusively TS$-7$

product$).$ Similarly, capacity for the TS$-8$ is six per day at all stations $($again$,$ assuming we

run only TS$-8).$ Five percent of TS$-8$ units must be reworked, which requires them to go

back through all three stations a second time $($process times are the same as those for the

first pass$).$ Reworked jobs never make a third pass through the line. There is no rework for

the TS$-7.$ Demand is three per day for the TS$-7$ and one per day for the TS$-8.$ The average

inventory level of chips is $20$ for the TS$-7$ and five for the TS$-8.$ Cycle time for both

cameras is four days, while the raw process time with no detractors is one$-$half a day.

Cameras are made to stock and sold from finished goods inventory. Average finished goods

inventory is four units of the TS$-7$ and one unit of the TS$-8,$ while the average backorder

level is $0\mathrm{.}29$ for TS$-7$ and $0\mathrm{.}12$ for TS$-8.$

$($a$)$ Compute throughput TH$($i$)$ for each station for each product.