Packaging at Amazon

You have just ordered $100$ items for a big project from an online retailer, say Amazon. Amazon is trying to determine the best batch size for processing this order, focusing on minimizing time until shipping.

Let us look at the details of this situation carefully. Suppose that it takes Amazon $10$ minutes to fetch an item from the warehouse, then it takes $50$ minutes per batch to get the paperwork in order plus $30$ minutes per batch to find and fetch the right size boxes and packing materials. Finally, it takes $6$ minutes per item to pack. Once all the items are packed the package is ready to be shipped.