Please show detailed work and answer question in sentence form. Thanks. Boise Cascade Corporation At the Boise Cascade Corporation, lumber mill logs arrive by truck and are scaled (measured to determine the number of board feet) before they are dumped into a log pond. The figure below shows the basic flow.

The mill manager must determine how many scale stations to have open during various times of the day. If too many stations are open, the scalers will have excessive idle time and the cost of scaling will be unnecessarily high. On the other hand, if too few scale stations are open, some log trucks will have to wait.

The manager has studied the truck arrival patterns and has determined that throughout the day, trucks randomly arrive at 16 per hour on average. Each scale station can scale 8 trucks per hour (7.5 minutes each). If the manager knew how many trucks would arrive during the hour, she would know how many scale stations to have open. For example, 0-8 trucks, open 1 scale station; 9-16 trucks, open 2 scale stations, etc.

However, the number of trucks is a random variable and is uncertain. Your task is to provide guidance for the decision.

1) Based on the mean rate of 16 trucks per hour, what probability distribution should be used?

2) Use the probabilities from the first probability distribution above to create a probability distribution for the number of scale stations to open. For example, 0-8 trucks, open 1 scale station; 9-16 trucks, open 2 scale stations, etc. What is the expected number of scale stations needed?

3) Are there additional factors that should be considered? What are your recommendations for handling those factors?

Boise Cascade Corporation At the Borse Cascade Corporation, lumber mill logs arrive by truck and are clied measured to determine the number of board feet) before they are dumped into a los pond. The figure below shows the basic flow The mill manager must determine how many scale stations to have open during various times of the day, if too many stations are open, the scalers will have excessive idle time and the cost of scaling will be unnecessarily high. On the other hand, too few scale stations are opery some log trucks will have to The manager has studied the truck arrival patterns and has determined that throughout the day, trucks Boise Cascade Corporation At the Borse Cascade Corporation, lumber mill logs arrive by truck and are clied measured to determine the number of board feet) before they are dumped into a los pond. The figure below shows the basic flow The mill manager must determine how many scale stations to have open during various times of the day, if too many stations are open, the scalers will have excessive idle time and the cost of scaling will be unnecessarily high. On the other hand, too few scale stations are opery some log trucks will have to The manager has studied the truck arrival patterns and has determined that throughout the day, trucks