A company purchases a component that is used in production. Annual demand is $60000$ units. Purchase price is $$10,$ order cost is $$100,$ lead time is one week, time dependent shortage cost is $$0\mathrm{.}33,$ time independent cost is $$20,$ inventory carrying cost rate is $0\mathrm{.}10.($a$)$ Determine the most approriate model, $($b$)$ calculate optimum lot size, reorder point, backorder level and total annual cost.