The inventory of Sheffield Company was destroyed by fire on March $1.$ From an examination of the accounting records, the following data for the first $2$ months of the year are obtained: Sales Revenue $$52,000,$ Sales Returns and Allowances $$1,000,$ Purchases $$34,000,$ Freight$-$In $$1,500,$ and Purchase Returns and Allowances $$1,700.$

Determine the merchandise lost by fire, assuming:

$($a$)$

A beginning inventory of $$22,000$ and a gross profit rate of $30\%$ on net sales.

Estimated cost of merchandise lost $