Liston, Inc., owns a factory located close to$,$ but not inside, a foreign trade zone. The plant imports volatile chemicals that are used in the manufacture of chemical reagents for laboratories. Each year, Liston imports about $$16,400,000$ of chemicals subject to a $30\%$ tariff when shipped into the United States. About $15\%$ of the imported chemicals are lost through evaporation during the manufacturing process. In addition, Liston has a carrying cost of $8\%$ per year associated with the duty payment. On average, the chemicals are held in inventory for $9$ months.

Assume that Liston is considering building a new plant inside a foreign trade zone to replace its chemical manufacturing plant.

$1.$ How much in duty and duty$-$related carrying costs will be saved by relocating inside the foreign trade zone?