Question

A warehouse measures 100 feet east-west and 200 feet north-south. The loading dock is in the southwest corner. Aisles run north-south. Items are uniformly distributed in the warehouse. To retrieve a single item, a worker must travel from the dock to the item’s location and back to the dock. The worker first goes east from the dock along the southern wall of the warehouse, then north along the aisle to the item and back, and returns westward to the dock.

(a) What is the average distance travelled to retrieve one item (to pick up the item and return with it to the dock)?

(b) What is the average distance travelled to get two items in one trip, assuming the items are in different aisles?

(c) What is the average distance travelled to get three items in one trip, assuming the items are in different aisles and assuming the first item retrieved is the westmost item and the third item retrieved is the eastmost item?

(d) What is the average distance travelled to get three items in one trip, assuming the items are in different aisles and assuming the second item retrieved is the westmost item and the third item retrieved is the eastmost item?

(e) Suppose items must be retrieved one at a time. If 1/8 of the items account for 90% of the retrievals, and you assign those items to the 50 foot by 50 foot square region in the southwest corner of the warehouse, what is the average distance travelled to retrieve one item?

Would someone give the complete and correct answer to the questions above please?

Answer 1