EOQ with Quantity Discounts $(20$ points$).$ County Hospital orders syringes from a hospital supply firm. The hospital expects to use $40,000$ per year. The cost to order and have the syringes delivered is $$800.$ The annual carrying cost is $$1\mathrm{.}90$ per syringe because of security and theft. The hospital supply firm offers the following quantity discount pricing schedule. Quantity Price $0-9999$ $$3\mathrm{.}4010,000-19,9993\mathrm{.}2020,000-29,9993\mathrm{.}0030,000-39,9992\mathrm{.}8040,000-49,9992\mathrm{.}6050,000+2\mathrm{.}40$ Determine the order size for the hospital that will minimize total costs. Show your work.