$(18$ points$)$

County Hospital orders syringes from a hospital supply firm. The hospital expects to use $40,000$ syringes per year. The ordering cost $($cost to order and have the syringes delivered$)$ is $$750$ per order. The annual holding cost per syringe is $25\%$ of the cost of a syringe. The hospital supply firm offers the following quantity discount pricing schedule.

$\backslash$table$[[$Order Quantity,Price per Syringe$],[0-7,999,$$$3\mathrm{.}46],[8,000-15,999,$$$3\mathrm{.}41],[16,000-23,999,$$$3\mathrm{.}39],[24,000$ and over,$$3\mathrm{.}36]]$

What is the optimal quantity per order based on the total annual cost $($composed of the holding cost and ordering cost and the acquisition cost$)?$ Provide the lowest total cost for each of the price options, include the holding, ordering and acquisition cost.