David's Delicatessen flies in Hebrew National salamis regularly to satisfy a grow$-$ ing demand for the salamis in Silicon Valley. The owner, David Gold, estimates that the demand for the salamis is pretty steady at $175$ per month. The salamis cost Gold $$1\mathrm{.}85$ each. The fixed cost of calling his brother in New York and having the salamis flown in is $$200.$ It takes three weeks to receive an order. Gold's account$-$ ant, Irving Wu$,$ recommends an annual cost of capital of $22$ percent, a cost of shelf space of $3$ percent of the value of the item, and a cost of $2$ percent of the value for taxes and insurance.

a$.$ How many salamis should Gold have flown in and how often should he order them?

b$.$ How many salamis should Gold have on hand when he phones his brother to send another shipment?

c$.$ Suppose that the salamis sell for $$3$ each. Are these salamis a proffable item for Gold? If so$,$ what annual profit can he expect to realize from this item? $($Assume that he operates the system optimally.$)$

d$.$ If the salamis have a shelf life of only $4$ weeks, what is the trouble with the pol$-$ icy that you derived in part $($a$)?$ What policy would Gold have to use in that case? Is the item still profitable?