Alter Templar is trying to use inventory models for his stores. He has $4$ stores in Philadelphia that sell printer papers. The City Hall store sells $100$ packets a day; the North Philadelphia store sells $50$ packets a day; the Whitman Plaza store sells $40$ packets a day, and the University City store sells $60$ packets a day. All of Alter's stores operate $365$ days a year. It costs Alter $$2$ per packet of paper from the supplier. Alter sells them for $$3.$ Alter's inventory carrying cost is $10\%$ of the unit cost per year. Alter does not see any variability in either demand or supplier's lead time.

Suppose Alter's supplier charges him $$10$ in order processing and delivery charges every time he places an order. Each of Alter's stores determines their order quantities separately.

$($a$)$ What is the EOQ for the City Hall Store? packets.

$($b$)$ What is the EOQ for the North Philadelphia Store? packets.

$($c$)$ What is the EOQ for the Whitman Plaza Store? packets.

$($d$)$ What is the EOQ for the University City Store: packets.

Alter is thinking about consolidating his orders. The vendor tells him that if he orders together for multiple stores, Alter will have to pay $$10$ in order processing and delivery charges for the first store, and then $$1$ for every additional store in the order. Suppose Alter orders for all $4$ stores together.