The soft goods department of a large department store sells $175$ units per month of a certain

large bath towel. The unit cost of a towel to the store is $$2\mathrm{.}50$ and the cost of placing an order

has been estimated to be $$12\mathrm{.}00.$ The store uses an inventory carrying charge of I $=27\%$ per

year. Determine $($a$)$ the optimal order quantity, $($b$)$ the order frequency, and $($c$)$ the annual

holding and setup cost. If$,$ through automation of the purchasing process, the ordering cost

can be cut to $$4\mathrm{.}00,$ what will be $($d$)$ the new economic order quantity, $($e$)$ the order frequency,

and $($f$)$ annual holding and setup costs?