An AGVS has three load/unload stations (numbered 1, 2, and 3) that form the corners of an equilateral triangle whose sides are each 1000 m long. The hourly rate of loads carried between stations is as follows: 20 loads from station 1 to station 2, 20 loads from station 2 to station 3, and 15 loads from station 3 to station 1. The From-To chart requires that the vehicles always move in one direction around the triangle (from 1 to 2 to 3 to 1 . . . ), so the traffic factor is assumed to be 1.0. Vehicle speed is 60 m/min. A total of 1.0 min is required for handling time per delivery (0.5 min for loading and 0.5 min for unloading). The AGVs must be scheduled as efficiently as possible, but the delivery requirements make it impossible to avoid some empty traveling by the vehicles. Assume that availability is 100%. Determine

(a) average delivery cycle time of a vehicle and
(b) how many vehicles are needed to meet the hourly delivery schedule.