Clever Cigar Seller
Mr. Cigarman sells fresh cigars at \($10\) each and re-rolled cigars at \($7\) each.
He buys his fresh cigars at \($800\) for a pack of 100 cigars. He makes re-rolled cigars himself. Each re-rolled cigar needs 4 used cigars costing \($1\) each and incurs a labour cost of \($2\) to make. Cigar butts can be re-rolled any number times.
Eg : If one starts with 20 cigars, the resultant 20 butts can be used to make 5 cigars. 4 of these 5 butts can be re-rolled again to get one more cigar.
If Mr. Cigarman buys 10 packs of cigars, and is only allowed to buy back the cigar butts that he sold to his customers, what is maximum amount of profit that he can earn from that stock.