this is the question, it is a multiple choice question

Answer the following multiple-choice problems. Circle only one answer for each part.

a) For the M/M/s queue, which of the following descriptions represents the utilization rate? a. The arrival rate per server divided by the service rate b. The arrival rate per server times the mean service time c. The overall arrival rate to the system divided by the product of the number of servers and the service rate d. All of the above (a through c) e. None of the above (a through c) b) For an M/M/s queue with a finite system capacity a. The value of =s must be strictly less than 1 b. The value of =s can be any non-negative value c. The value of =s must be strictly more than 1 d. The value of =s is undefined. c) For an M/M/s queue (with infinite capacity), the variability of the simulated total time in the system a. Increases with the utilization ratio b. Is independent of the utilization ratio c. Decreaases with the utilization ratio. d) For an M/M/s queue (with infinite capacity) the waiting time in the queue prior to service (Wq) a: Goes up with the utilization ratio (holding s and constant) b. Goes up with standard deviation of the service time distribution (holding all else constant) c. Is independent of the variance of the service time distribution d. Goes down as the number of servers goes up, holding =s constant. e. Is independent of the value of =s f. Answers (a), (b), and (d) above. g. All of answers (a) through (e) h. None of answers (a) through (e) e) The number of people that are likely to attend a special history lecture follows a Poisson distribution with a mean of 30 , how many seats should the sponsor set up to be at least 95% sure that there will be enough seats for everyone who shows up. Pick the smallest value from the options below that ensures this condition is met. a. 60 seats b. 50 seats c. 40 seats d. 35 seats e. 30 seats f. There is not enough information to answer this question. f) Consider a newsvendor problem. The demand for the product follows a Poisson distribution with a mean of 30 . You buy the item from the supplier at a cost of $100 and you sell each item for $220. The salvage value of any unsold items is $60. The optimal number to buy is: a. 30 items b. 27 items c. 34 items d. 40 items e. We do not have enough information to answer this question. g) Using the newsvendor data shown in problem (f), the expected profit is (too the nearest hundred dollars): a. $4080 b. $3600 c. $3400 d. $3300 e. $3200 f. $3000 g. We need more information