A NC lathe cuts two passes across a cylindrical workpiece under an automatic cycle. The operator loads and unloads the machine. The starting diameter of the work is 3.00 in, and its length is 10 in. The work cycle consists of the following steps (with element times given in parentheses where applicable):

1. Operator loads part into machine and starts cycle (1.00 min).
2. NC lathe positions tool for the first pass (0.10 min).
3. NC lathe turns first pass (time depends on cutting speed).
4. NC lathe repositions tool for the second pass (0.4 min).
5. NC lathe turns second pass (time depends on cutting speed).
6. Operator unloads part and places it in the tote pan (1.00 min).

In addition, the cutting tool must be periodically changed, taking 1.00 min. The cost of the operator and machine is $39/hr. The tool cost is $2.00 per cutting edge. The feed rate is 0.007 in/rev, and the depth of cut for each pass is 0.100 in. The applicable Taylor tool life equation parameters are: \( n = 0.26 \) and \( C = 900 \) (ft/min).

Determine:
a) The cutting speed for minimum cost per piece.
b) The average time required to complete one production cycle.
c) The cost of the production cycle.
d) If the setup time for this job is 3.0 hours and the batch size is 300 parts, how long will it take to complete the batch?