$(12$ points$)$ Best Buy is optimizing its inventory strategy for a popular laptop model. Here are the key inventory management details:

Annual Demand for the Laptop: $18,000$ units.

Cost per Laptop: $$800.$

Inventory Carrying Cost: $$40$ per unit per year.

Average Ordering Cost: $$150$ per order.

Lead Time: $4$ days.

Store Operating Days: $360$ days per year.

Using these specifics, calculate the following:

a$.(3$ points$)$ Economic Order Quantity $($EOQ$)$

b$.(2$ points$)$ Optimal number of orders per year

c$.(2$ points$)$ Optimal number of days between orders

d$.(5$ points$)$ Total inventory cost including the cost of buying the $18,000$ units per year