### Buying in Rocket Ships and Selling in Fire Sale

Source: Asked to me by Ankush Jain (CSE IITB 2011, Morgan Stanley Quant Associate). He took it from Algorithms Design book by Tardos and Kleinberg Problem: Easy case: You’re trying to buy equipments whose costs are appreciating. Item i appreciates at a rate of r_i > 1 per month, starting from $100, so if you buy it t months from now you will pay 100*((r_i)^t) . If you can only buy one item per month, what is the optimal order in which to buy them? Difficult case: You’re trying to sell equipments whose costs are depreciating . Item i depreciates at a rate of r_i < 1 per month, starting from $100, so if you sell it t months from now you will get 100*((r_i)^t) . If you can only sell one item per month, what is the optimal order in which to sell them?