Reference no: EM132323729

Question 1: Sam Certo, a Nanaimo vet, is running a rabies vacci¬nation clinic for dogs at the local grade school. Sam can "shoot" a dog every three minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of one dog every six minutes according to a Poisson distribution. Also assume that Sam's shooting times are exponentially distributed. Compute the following:
a) The probability that Sam is idle.
b) The proportion of the time that Sam is busy.
c) The average number of dogs being vaccinated and waiting to be vaccinated.
d) The average number of dogs waiting to be vaccinated.
e) The average time a dog waits before getting vaccinated. F)The average amount of time a dog spends waiting in line and being vaccinated.

Question 2: Automobiles arrive at the drive-through window at the downtown. Fort McMurray post office at the rate of four every 10 minutes. The average service time is two minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed.
a) What is the average time a car is in the system?
b) What is the average number of cars in the system?
c) What is the average number of cars waiting to receive service?
d) What is the average time a car is in the queue?
e) What is the probability that there are no cars at the window?
f) What percentage of the time is the postal clerk busy?
g) What is the probability that there are exactly two cars in the system?
h) By how much would your answer to part (a) be reduced if a sec¬ond drive-through window, with its own server, were added?

Question 3: Baker Mfg Inc. (see Table 11.8) wishes to compare its inventory turnover to those of industry leaders, who have turnover of about 13 times per year and 8% of their assets invested in inventory.

a) What is Baker's inventory turnover?
b) What is Baker's percentage of assets committed to inventory?
c) How does Baker's performance compare to the industry leaders?

Table 11.8
For Problems 11.11 and 11.12

Question 4: The grocery industry has an annual inventory turnover of about 14 times. Organic Grocers, Inc., had a cost of goods sold last year of $10.5 million; its average inventory was $1.0 million.

What was Organic Grocers's inventory turnover, and how does that performance compare with that of the industry?

Question 5: Hau Lee Furniture, Inc., spends 60% of its sales dollars in the supply chain and has a current gross profit of $10,000. Hau wishes to increase gross profit by $5,000 (50%). He would like to compare two strategies: reducing material costs vs. increasing sales. The current material costs and production costs are 60% and 20%, respectively, of sales dollars, with fixed cost at a constant $10,000. Analysis indicates that an improvement in the supply chain that would reduce material costs by 8.3% ($5,000/$60,000) would produce a 50% net profit gain for Hau, whereas a much larger 25% increase in sales ($25,000/$100,000) would be required to produce the same result. Now Hau finds its current profit of $10,000 inadequate. The bank is insisting on an improved profit picture prior to approval of a loan for some new equipment. Hau would like to improve the profit line to $25,000 so he can obtain the bank's approval for the loan.

What percentage improvement is needed in the supply chain strategy for profit to improve to $25,000?

What is the cost of material with a $25,000 profit?

What percentage improvement is needed in the sales strategy for profit to improve to $25,000? What must sales be for profit to improve to $25,000?

Question 6: Bloom's Jeans is searching for new suppliers, and Debbie Bloom, the owner, has narrowed her choices to two sets. Debbie is very concerned about supply disruptions, so she has cho¬sen to use three suppliers no matter what. For option 1, the suppliers are well established and located in the same country. Debbie calculates the "unique event" risk for each of them to be 4%. She estimates the probability of a nationwide event that would knock out all three suppliers to be 2.5%. For option 2, the suppliers are newer but located in three different countries. Debbie calculates the "unique event" risk for each of them to be 20%. She estimates the "super-event" probability that would knock out all three of these suppliers to be 0.4%. Purchasing and transportation costs would be $1 000 000 per year using option 1 and $1 010 000 per year using option 2. A total disruption would create an annualized loss of $500 000.

a) What is the probability that all three suppliers will be disrupted using option 1?

b) What is the probability that all three suppliers will be disrupted using option 2?