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A pharmacist wants to establish an optimal inventory policy for a new antibiotic that requires refrigeration in storage. The pharmacist expects to sell $4800$ packages of this antibiotic at a steady rate during the next year. She plans to place several orders of the same size spaced equally throughout the year. The ordering cost for each delivery is $$12,$ and carrying costs, based on the average number of packages in inventory, amount to $$8$ per year for one package. Use this information to answer the following questions.

$($a$)$ Let $x$ be the order quantity and $r$ the number of orders placed during the year. Find the inventory cost $($ordering cost plus carrying cost$)$ in terms of $x$ and $r.$

$C=$

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