A workshop produces a medium and high variety of products. A certain part is required to go through 8 processes sequentially in different 8 machines. 20 batches, each consisting of 30 products, will be produced each week. The factory works 70 hours per week, with an average operation time of 8 hours, an average setup time of 6 hours, and an average non-operation time of 12 hours per batch. In the factory, there are 24 machines in the plant working in parallel. The plant operates an average of 70 production hours per week.
a) What is the manufacturing lead time for the factory?
b) What is the plant capacity?
c) Determine the plant utilization?