Saram Lanka makes winch components for its different product lines. The firm operates its production facility $250$ days per year. It has orders for about $12,000$ winch components per year and has the capability of producing $100$ per day. Setting up the winch production costs $$50.$ The cost of each winch component is $$1.$ The holding cost is $$0\mathrm{.}10$ per winch component per year. The firm$$s operations manager wants to calculate the:

a$)$ Economic production quantity

b$)$ Annual holding costs

c$)$ Annual ordering costs

d$)$ Total inventory costs