A partially automated production line has a mixture of three mechanized and three manual workstations. There are a total of six stations, and the ideal cycle time of 1.0 min, which includes a transfer time of 6 sec. Data on the six stations are listed in the accompanying table. Cost of the transfer mechanism Cat = $0.10/min, cost to run each automated station Cas = $0.12/min, and labor cost to operate each manual station Cw = $0.17/min. It has been proposed to substitute an automated station in place of station 5. The cost of this station is estimated at Cas5 = $0.25/min and its breakdown rate p5 = 0.02, but its process time would be only 30 sec, thus reducing the overall cycle time of the line from 1.0 min to 36 sec. Average downtime per breakdown of the current line, as well as for the proposed configuration, is 3.5 min. Determine the following for the current line and the proposed line:
(a) Production rate,
(b) Proportion uptime, and
(c) Cost per unit. Assume the line operates without storage buffers, so when an automated station stops, the whole line stops, including the manual stations. Also, in computing costs, neglect material and tooling costs.

Station Type Manual Automatic Automatic Automatic Manual Manual Process time 36 sec 15 sec 20 sec 25 sec 54 sec 33 sec 0.01 0.02 0.01 4