Question $9$

Study the scenario and complete the questions that follow.

Inventory

Dischem pharmacy wants to establish an optimal inventory policy for a new antibiotic that requires refrigeration in storage. The pharmacy expects to sell $800$ packages of this antibiotic at a steady rate during the next year. The pharmacy plans to place several orders of the $($same size spaced equally$)$ throughout the year. The ordering cost for each delivery is R$16,$ and carrying costs, based on the average number of packages in inventory, amount to R$4$ per year for one package.

Slightly adjusted source: Goldstein, $1\mathrm{.}2009.$ Calculus and H$=$s Applications. $14"$ Edition. USA: Pearson. Page $175.$

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 $r.$ Explain your answer.

b$.$ Determine the constraint function. Justify your answer.

$(3$ Marks$)$

c$.$ Determine the economic order quantity that minimizes the inventory cost, and then find the minimum inventory cost.

$(8$ Marks$)[$Sub Total $14$ Marks$]$