Trade

In a certain kingdom, a merchant traded a particular good. He lived and prospered until the king decided to impose a tax on each transaction, set at $p$ per-$q$-cent of the transaction amount (i.e., $p/q$ of the transaction amount). If the tax is not an integer, it must be rounded to the nearest integer. If there are two nearest integers, the larger one is chosen.

The merchant has $N$ units of goods, each priced at $c$. Any number of customers may come, each able to buy any number of goods. The merchant trades until he has sold all his goods.

As the goods have not yet gone on sale, the merchant wants to estimate the minimum and maximum amounts he can receive for his goods after taxes are deducted, and asks for your help.