Without help, it typically takes between one and three solid weeks of research and writing time:

SBA estimates it will take you 520 hours (10 hours per response). While we feel that estimate is too high, it gives a good idea of the level of detail that SBA is expecting to see.

Without our assistance, it typically takes the average 8(a) company owner between 40 and 100+ hours of research and writing time to prepare his/her own 8(a) Business plan. The problem, of course, is that it involves your time. You are the owner of the firm - the person whose time is most valuable and who can least afford to turn your attention away from running your business even for a days - let alone a few weeks.

Can I delegate the task to a subordinate?

Probably not.  A subordinate - if one is available - is unlikely be able to adequately address the many complex questions about your 8(a) business development objectives in a manner acceptable to SBA.  Unless someone is familiar with what SBA is looking for and how to address it, they will probably miss the mark on the first try - leading to multiple revisions, wasted time and lost opportunities.