Consider the following conditions:

$(1)$ When an order is placed by Purdue Company, Indiana Company delivers products to Purdue

Company continuously with a delivery rate $()$ of $4,800$ units per year. The delivery starts $10$ days after

the order date $($i$.$e$.$ LT $=10$ days$).$

$(2)$ Purdue Company$$s maximum shortage $($ max $)$ is $20$ units.

$(3)$ Purdue Company operates $320$ days a year.

$($a$)$ Determine the optimal order quantity $($

$*)$ of Purdue Company.

$($b$)$ Determine the maximum inventory level $($ max $)$ using the optimal order quantity.

$($c$)$ Determine the number of operating days between orders using the optimal order quantity.

$($d$)$ Determine the reorder point in the number of units when the company orders the optimal quantity