A fertilizer plant acquires phosphate from a single source. The plant's weekly phosphate requirement has a

normal distribution with a mean of $720$ metric tons and a standard deviation of $20$ metric tons. The lead time for

phosphate supply is $9$ days $($ ~~$1\mathrm{.}286$ weeks$).$ To place an order, an administrative employee spends around one

hour reviewing the inventory level, preparing the order, tracking the delivery, and updating records. When the

delivery is received, it takes roughly one worker hour to unload, inspect, and store the material in a warehouse.

The administrative staff member is paid $$25$ per hour and the warehouse employees are paid $$16$ per worker

hour. Delivery charges are $$650$ per shipment. The company purchases phosphate at $$400$ per metric ton. The

annual cost of capital is $4\mathrm{.}5\%.$ Other holding costs are negligible. How much should the plant order at a time?

What will be the Reorder Point if the desired service level during the lead time is $95\%?$

$($Consider $52$ weeks in a year for planning. Show your working for the answers.$)$