City Guilds Model Questions Vol1 2020 Engineering Question 11

A workshop must produce 5,000 identical steel shafts (each 150 mm long, 20 mm diameter). Two possible manufacturing processes are considered: **Process T (turning)** - tool life follows \( V T^{0.25}=200 \) (V in m min\(^{-1}\), T in min). Cutting speed V may be chosen between 30 and 80 m min\(^{-1}\). Machining time per shaft is \( t=\frac{0.2}{V}\) min. Tool cost is ₦1,500 per carbide insert. Machine hourly cost is ₦2,500. Setup time per batch is 30 min and a batch can contain at most 200 shafts before a tool change. **Process M (milling)** - tool life follows \( V T^{0.20}=120 \). Cutting speed V may be chosen between 20 and 60 m min\(^{-1}\). Machining time per shaft is \( t=\frac{0.12}{V}\) min. Tool cost is ₦800 per end‑mill. Setup time per batch is 20 min and a batch can contain at most 150 shafts before a tool change. Machine cost is the same as above. Both processes must complete the whole order within 1,200 min (including all setups and tool changes). Determine which process can meet the time requirement and give the minimum total cost (tool cost plus machine operating cost) for that process. State the process name and the total cost in naira.