Show me the steps to solve Ramen Inc. adopted dollar$-$value LIFO $($DVL$)$ as of January $1,2011,$ when it had a cost inventory of $$600,000.$ Its inventory as of December $31,2011,$ was $$667,800$ at year$-$end costs and the cost index was $1\mathrm{.}06.$ What was DVL inventory on December $31,2011?$