A caterer known that he will need 40 napkins on a given day and 70 napkins the day after. He can purchase napkins at 20 paise each and after they are purchased , he can have dirty napkins laundered at 5 paise eachfor use next day. In order to minimize his cost how many napkins should be purchased initially and how many dirty napkins should he have lunndered?

If he buys 70 napkins, he'll have to pay 1400 paise, 40 of which he'll be laundering, costing him 200 paise, for a total of 1600 paise.

Now, if he buys 71 napkins, and launders 39 (he's throwing 1 dirty napkin away), he'll be paying a total of 1615 paise.

For each additional napkin he buys, he'll pay 15 paise more. So, the minimum remains 70 napkins bought, with 40 laundered.