1. A distribution center uses 10 delivery trucks to transport shipment orders to two cities. 2. When an order is phoned in, a delivery truck leaves with that order (and only that order) if a delivery truck is available. If a delivery truck is not available, then the order is "lost," that is, it is routed to another distribution center. If a delivery truck is available, then the truck enters a queue to get loaded. The loading station currently has one "loader" to load one truck at a time. It takes 100 units of time to pack a truck if the truck is a "full" truck and 50 units of time to pack a truck if the truck is not a "full" truck. Forty percent of the trucks are "full" trucks and sixty percent are not "full" trucks. 3. 50% of the deliveries are to City 1 and 50% are to City 2. The time it takes a truck to travel to City1 or City2, deliver the shipment and return is exponentially distributed. The mean time for City1 is 100 units of time and for City 2 is 200 units of time. 4. The inter-arrival time for shipment orders is exponentially distributed with a mean of 50 units of time. A diagram of the outline of this system is provided at the bottom of this file.

What is the minimum number of loaders that would be necessary to achieve the minimum average utilization rate of the ten delivery trucks? Use three significant digits to measure the rate. That is, answer this question using this measure as a proportion measured to 3 decimals. ANSWER____________________________________ 5. Using the number of loaders found in the previous part, what is the total number of trucks that completed trips to City1 and to City2? ANSWER for City 1_________________________________ ANSWER for City2_________________________________ 6. How many supply orders were "lost" due to non-availability of supply trucks with the number of loaders stated in your answer to part 4? ANSWER _________________________________