Weekly demand for a certain product is normally distributed with a mean of $420$ and standard deviation of $9.$ The source of supply is reliable and maintains a constant lead time of $3$ weeks. The cost of placing the order is $$20$ and annual holding costs are $$2\mathrm{.}50$ per unit. There are no stockout costs and unfulfilled orders are filled as soon as the order arrives. Assume that sales occur over entire $52$ weeks over a year. Find:

Part $1$: $(1$ mark$)$ Calculate Economic Order Quantity $($EOQ$)$

Part $2$: $(1$ mark$)$ Calculate Reorder Point $($use $z=1\mathrm{.}65)$

Part $3$: $(0\mathrm{.}5$ mark$)$ What is average on hand inventory

Part $4$: $(0\mathrm{.}5$ mark$)$ How many orders will be placed per year if we order the BOQ quantity every time?

Part $5$ : $(0\mathrm{.}5$ mark$)$ If the cost per unit is equal to $S\frac{30}{?}$ unit, calculate the total annual purchasing cost

Part $6$: $(1$ mark$)$ Calculate the total annual cost

Part $7$: $(0\mathrm{.}5$ mark$)$ State the inventory policy