The manager of a car wash received a price list from the vendor who supplies soap. Annual usage of soap is $4,500$ gallons.The ordering cost is $$30$ per order and annual carrying cost is $60\%$ of the purchase price of soap per gallon. The price list $($cost per gallon$)$ is shown in the following table.QuantityUnit Price$1-399$$$3\mathrm{.}10400+$$$2\mathrm{.}75$What is the optimal order quantity?