City Guilds Model Questions Vol1 2023 Engineering Question 39

A batch of 500 steel shafts (each 150 mm long) must achieve a surface roughness of \(R_a \le 0.8\,\mu\text{m}\). Two processes are considered:\n\n(i) CNC turning: tool‑change cost \(\text{₦}200\) per shaft, machining cost \(\text{₦}150\) per hour, machine availability 80 %. The average cutting speed is 120 m/min, feed 0.2 mm/rev, depth of cut 2 mm. The initial diameter is 50 mm and the final diameter 48 mm.\n\n(ii) Grinding: per‑shaft cost \(\text{₦}300\), grinding cost \(\text{₦}250\) per hour, machine availability 90 %, and each shaft requires 0.30 h of grinding time. Grinding can achieve the required roughness directly.\n\nWhich process gives the lower total production cost? Show all calculations and give the total cost for each process (rounded to the nearest naira).