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Chapter 6- Solved Problems Problem 1 Customers arrive at a bank drive-up window every 3.5 minutes based on a Poisson distribution. Once they arrive at the teller, service time is exponentially distributed based on a rate of 4 minutes per transaction, a. What is the probability that a customer will not have to wait for service? b. How many customers are most likely in line (waiting) at any one point in time? c. What will be the average time waiting in the system? d. What will be the average time in the system? Answer Problem 1 T n T = 12.5% A. Pn n! B. Cw 2 = 6.125 people C. Tw = 1.75 min D. Ts 1 = 2 min Problem 2 A company is selecting among three alternative capacity plans. The first alternative is a job shop with low fixed costs ($250,000), but with highly skilled labor higher variable cost per unit ($18). The second alternative is a form of cellular manufacturing with fixed cost of $325,000 and variable cost of $14 per unit. The third consideration is a product layout. This will cost $500,000 to set up, but result in a variable cost of only $7.50 per unit. Which layout should be selected at the following volumes (a) 10,000, (b) 20,000 , (c) 30,000. Answer Problem 2 Job vs. Cell 250,000 + 18X = 325,000 + 14X X = 18,750 Cell vs. Product 325,000 + 14X = 500,000 + 7.5X X = 26,923.07 A. A job shop is best at 10,000 units B. A cell would be best for 20,000 units C. A product layout would be best for 30,000 units Problem 3 A beverage supply company is trying to determine the appropriate stocking level for an upcoming festival to be held in town. Based on historic data, the company predicts that there is a 30% chance that the festival will attract 20,000 customers (small); a 40% chance that it will attract 45,000 (medium); a 20% chance that it will attract 60,000 (large); and a 10% chance it will attract 75,000 (huge). Assuming that each customer represents one sale of $5, what is the value of the festival for the company? Answer Problem 3 Size Small Medium Large huge EMV = $217,500 Probability .30 .40 .20 .10 Customers 20000 45000 60000 75000 Value 30000 90000 60000 37500