Problem $5$:

Central University uses $$123,000$ of a particular toner cartridge for laser printers in the student computer labs each year. The purchasing director of the university estimates the ordering cost at $$45$ and thinks that the university can hold this type of inventory at an annual storage cost of $22\%$ of the purchase price. How many months' supply should the purchasing director order at one time to minimize the total annual cost of purchasing and carrying?

$((($How do i know how many months supply should the purchasing director order$($how to calculate it$,$ based on what$)))$