Operations Research

Problem 1. Two one-man barber shops sit side by side in Dunkirk Square. Each can hold a maximum of 4 people, and any potential customer who finds a shop full will not wait for a haircut. Barber 1 charges $11 per hair haircut and takes an average of 12 minutes to complete a haircut. Barber 2 charges $5 per haircut and takes an average of 6 minutes to complete a haircut. An average of 10 potential customers per hour arrive at each barber shop. Of course, a potential customer becomes an actual customer only if he finds that the shop is not full. Assuming that interarrival times and haircut times are exponential, which barber will earn more money? How much more? Answer: _____________________ ________________________

Problem 2. In this problem, all interarrival and service times are exponential. a. At present, the finance department and the marketing department each have one typist. Each typist can type 25 letters per day. Finance requires that an average of 20 letters per day be typed, and marketing requires that an average of 15 letters per day be typed. For each department, determine the average length of time elapsing between a request for a letter and completion of the letter. Answer: Finance ________________________, Marketing _________________________ b. Suppose that the two typists were grouped into a typing pool; that is, each typist would be available to type letters for either department. For this arrangement, calculate the average length of time between a request for a letter and completion of the letter.

Answer: ____________________________ c. Under the pooled arrangement, what is the probability that more than 0.200 day will elapse between a request for a letter and completion of the letter? (Answer: 0.0688)

Answer: _____________________________ Problem 3. My dog just had 3 frisky puppies that jump in and out of their whelping box. A puppy spends an average of 10 minutes (exponentially distributed) in the whelping box before jumping out. Once out...