ABC is the owner of a small company that produces electric knives used to cut fabric. The annual demand is $10000$ for knives, and ABC produces the knives in batches. On average, ABC can produce $80$ units per day, the number of working days in a year is $300$ days. The cost to set up the production process is VND $3\mathrm{.}000\mathrm{.}000,$ and it costs the company VN$5\mathrm{.}200/$unit$/$month$.$ Know that, at the start of every batch production the inventory is $200$ units.

a$.$ How many knives should ABC produce in each batch?

b$.$ What is the maximized inventory of the company?

c$.$ What is the total annual set up cost and holding cost?