please solve with all steps written down and clear all manually showing from where we got each value. thank you

8 A plant manufactures three parts, A, B, and C, to be assembled into a product. Turret lathes are required for one operation on each of the three. For planning purposes it is as- sumed that plant personnel work at 70 percent of normal and lathes have a utilization probability of 0.90. Policies establish that no run will be for less than the monthly pro- duction requirement. The plant works an 8-hour, 5-day week, and setup is carried out during the regular work shift. The required production is 10,000 per month (4.2 weeks/month). It is desired to determine: (a) the number of lathes; (b) the number of turret lathe operators; (c) the number of turret lathe setup workers. The following data are given (including setup time per machine): Product Operation Time (h) Defective (%) Setup time(h/month) A B A-747 B-214 C-103 0.083 0.031 0.117 3.4 2.6 1.5 10 14 12