The management of Tyron Inc. is contemplating changing it inventory policy. Right now, Tyron Inc. has $$31,000$ in current assets and $$22,000$ in current liabilities and its initial inventory level is $$8,000.$ Tyron Inc. wants to rise funds as additional notes payable and use them to increase inventory but whatever funds they raise and invest them in inventory, they must make sure their new current ratio stay above $1\mathrm{.}10$ in order to maintain their credit rating. Giving this, what is the maximum new level of inventory for Tyron $($so that they do not go below a current ratio of $1\mathrm{.}10?$