$5.$ Consider a line that makes two different digital TVs$.$ The DTV$-15$ costs $ $4,500$ while the DTV$-25$ costs $ $8,000.$ In manufacturing both TVs go through the same three steps but take different amounts of time. The capacities for the DTV$-15$ are $10,6,$ and $8$ per day at workstations $1,2,$ and $3$ respectively when DTV$-15$ is run exclusively on these workstations. Similarly, capacity for the DTV$-25$ is $5$ per day at all stations when it is run exclusively on these workstations. Seven percent of DTV$-25$ must be reworked, sending them through all the three workstations and the process times are the same as those for the first pass. Reworked jobs never make a third pass through the line. For the DTV$-15,$ three percent must be reworked under similar conditions.

Demand is five per day for DTV$-15$ and two per day for DTV$-25.$ The average inventory levels are $15$ and $5,$ respectively. Cycle time for both TVs is five days while the raw process time is $1$ day. TVs are made to stock and sold from finished goods inventory. The average finished goods inventory is $10$ and $3$ respectively, while the fill rate is $0\mathrm{.}8$ for both the TVs$.$

a$)$ Compute the efficiencies Ec$,$ EI$,$ and ET$.$

b$)$ Suppose the machine at workstation $1$ costs $ $1\mathrm{.}5$ million and the machines at the second and the third stations cost $ $100,000$ each. Compute Cc and contract with Ec computed above.