Statement

The washing machine has been broken for a week, so laundry has accumulated. You must divide the clothes into piles. Each item has a drying time T_i, and each pile may contain at most C items (the machine capacities). The piles are washed sequentially, and each wash takes W time. After a pile is washed, it is placed immediately into the drying machine. A pile finishes drying when its slowest item finishes. The next pile cannot begin drying until the previous one has fully dried, so the drying machine must be empty before the next pile is placed. Loading and unloading the machine takes 0 time. Find a partition of the clothes into piles that minimizes the total time to wash and dry all items.