Westside Auto purchases a component used in the manufacture of automobile generators directly from the supplier. Westside$$s generator production operation, which is operated at a constant rate, will require $30000$ components per month throughout the year.

Assume that the ordering costs are $$800$ per order,

the unit cost is $$10\mathrm{.}00$ per component,

and annual holding costs are $25\%$ of the value of the inventory.

Westside has $300$ working days per year and a lead time of $14$ days. Answer the following inventory policy questions:$2.$ Economic Production Lot Size model:

$1)$ What type of inventory costs will be considered?

$2)$ To reach the optimal lot size, what cost will be minimized?

$3)$ If D $=28,000$ units per year and P $=40,000$ units per year, how much would be the utilization factor? Will the machines be idle for a while or the machines will be running throughout the whole year? How much percentage of the time will the machines be idle?