A production system consists of four machines and three buffers between machines. Parts entering the system require processing by each of the four machines in a serial fashion. A part is always available for processing at the first machine. After a part is processed, it moves from the machine to the buffer storage area for the next machine, where it waits to be processed. However, if the buffer is full, the part cannot move forward and remains on the machine until a space becomes available in the buffer. Furthermore, the machine is blocked and no other parts can move to the machine for processing. The part exits the system after being processed by the fourth machine. Note that parts are selected from buffers to be processed by a machine in a FIFO order. The processing time at each machine is exponentially distributed with a mean of 1.0 minute, 1.3 minutes, 0.7 minute, and 1.0 minute for machines 1, 2, 3, and 4, respectively. The time to move parts from one location to the next is negligible. The goal is to find the optimal size of each buffer to maximize the profit made from the sale of parts. The manufacturer collects $10 per part produced (out of the system). The limitation is that each unit of space for a part in a buffer costs, $1000 (i. e. each space allocated in a buffer has a fixed cost of $1000). So the buffer storage has to be strategically allocated to maximize the throughput of the system. The throughput will be measured as the number of parts completed during a 30-day period. Develop a simulation model to determine the optimal size of each buffer that maximizes the manufacturer profit in the steady state. Start the search with all buffer sizes equal to 8. Run the simulation for 30 replications, a replication length of one year each, and a warm up period of 15 days. Use process analyzer to evaluate different combinations of the buffer at each station. Please use Arena to build the model. Or draw the diagram with detailed information.