Task $2$: A fertilizer plant acquires phosphate from a single source. The plant$$s weekly phosphate requirement has a normal distribution with a mean of $850$ metric tons and a standard deviation of $25$ metric tons. The lead time for phosphate supply is $15$ days. To place an order, an administrative employee spends around one hour reviewing the inventory level, preparing the order, tracking the delivery, and updating records. When the delivery is received, it takes roughly one worker hour to unload, inspect, and store the material in a warehouse. The administrative staff member is paid $$26$ per hour and the warehouse employees are paid $$18$ per worker hour. Delivery charges are $$650$ per shipment. The company purchases phosphate at $$500$ per metric ton. The annual cost of capital is $5\%.$ 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.$)$

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