When Mary Potts arrived at her store on the morning of January $29,$ she found empty shelves and display racks; thieves had broken in during the night and stolen the entire inventory. Accounting records showed that Potts had inventory costing $$56,000$ on January $1.$ From January $1$ to January $28,$ Potts had made net sales of $$78,400$ and net purchases of $$89,600.$ The gross profit during the past several years had consistently averaged $43$ percent of net sales. Potts plans to file an insurance claim for the theft loss.

Required:

a$.$ Using the gross profit method, estimate the cost of inventory at the time of the theft.