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Why should dollar and relative differences be used jointly in variance analysis?

The owner of Firewood To Go is considering buying a hydraulic wood splitter which sells for $50,000. He figures it will cost an additional $100 per cord to purchase and split wood with this machine, while he can sell each cord of split wood for $125. How many cords of wood would he have to split with this machine to make a profit of $30,000?

Customers arrive at a suburban ticket outlet at the rate of 14 per hour on Monday mornings. This can be described by a Poisson distribution. Selling the tickets and providing general information takes an average of 3 minutes per customer, and varies exponentially. There is 1 ticket agent on duty on Mondays. What is the average number in line? 

During the early morning hours, customers arrive at a branch post office at an average rate of 45 per hour (Poisson), while clerks can handle transactions in an average time (exponential) of four minutes each. If clerk cost is $30 per hour and customer waiting time represents a “cost” of $20 per hour, how many clerks can be justified on a cost basis?

Customers arrive at a suburban ticket outlet at the rate of 14 per hour on Monday mornings. This can be described by a Poisson distribution. Selling the tickets and providing general information takes an average of 3 minutes per customer, and varies exponentially. There is 1 ticket agent on duty on Mondays. What is the average time in the system?

A chance node on a decision tree has four possible outcomes, each worth $100,000. The probabilities of the outcomes occurring are assessed as 10%, 27%, 43%, and 20%. What is the expected value of this chance node?

A production manager at Ultra Clean Dishwashing Company is monitoring the quality of the company’s production process. There has been concern relative to the quality of the operation to accurately fill the 16 ounces of dishwashing liquid. A common requirement in this industry shows that the tolerance should be 5% of the expected volume (±5%). The study of the production process returns the process mean (15.8) and standard deviation (0.3). What is the probability of generating a defect?

During the early morning hours, customers arrive at a branch post office at an average rate of 45 per hour (Poisson), while clerks can handle transactions in an average time (exponential) of four minutes each. The average number of customers waiting for service if six clerks are used is

In monitoring process quality, we might use which of the following statistics?

A bank of 10 machines requires regular periodic service. Machine running time and service time are both exponential. Machines run for an average of 44 minutes between service requirements, and service time averages six minutes per machine. If operators cost $15 per hour in wages and fringe benefits and machine downtime costs $75 per hour in lost production, what is the optimal number of operators for this bank of machines?