Billy of Billy’s Warehouse in Maine contracts with motor carriers for deliveries however, they assess him with stiff penalties if their trucks have to wait to be unloaded. He thought about investing significantly in technology and equipment to improve productivity. The following facts apply to his situation: 1) Trucks arrive randomly at the average rate of five per hour, with a deviation of plus or minus one. 2) A team of 2 warehouse workers can unload trucks at the rate of 6 per hour, or one every 10 minutes. 3) A team of 4 warehouse workers can unload trucks at the rate of 8 per hour, or one every 7.5 minutes 4) A team of 6 warehouse workers can unload trucks at the rate of 10 per hour, or one every 6 minutes 5) A team of 8 warehouse works can unload trucks at the rate of 12 per hour, or one every 5 minutes. 6) Because of its contract with the carriers, the warehouse must pay the motor carrier that own idle trucks at the rate of $100 per hour while the trucks stand idle, waiting to be unloaded. 7) The number of teams or servers is always 1, although the number varies in terms of costs and output. Part A: Using the queue theory, for each of the four work team sizes, calculate the expected number of trucks waiting in the queue to be unloaded and calculate the expected time in the queue- that is the expected time a truck has to wait in line to be unloaded. (Lay out all costs in tabular form.) Part B: Using the number of trucks in queue and the expected time a truck has to wait, along with the rate per hour that he must pay for idle time, determine how much Billy is losing with idle trucks with each of the work teams. (Lay out all costs in tabular form) Part C: Using what you have learned in the text concerning warehouse productivity, how can Billy improve his warehousing productivity without significant investment in technology or equipment?