Question

1) Consider the following distribution and random numbers: Demand Frequency 0.15 0.30 0.25 0.15 0.15 Random Numbers; 62 13 25 40 0 4 What four demand values would be developed from the random numbers listed? 2) Given the following random number ranges and the following random number sequence: 62, 13, 40, 86, 93, determine the expected average demand for the following distribution of demand. Random Demand Number Ranges 00-14 15-44 45-69 70-84 85-99 Answer:_ The number of cars arriving at Joe Kelly's oil change and tune-up place during the last 200 hours operation is observed to be the following: Number of 3 or less 10 Cars Arriving Freque ncy 10 30 70 50 40 9 or more 3. Determine the probability distribution of car arrivals. Use table below for your answers. Number ofProbability of CarsOccurrence Arriving 4, Based on the above frequencies, use two-digit random numbers, start with random number 00, a determine the random number ranges for the data set given above. Use the table below for your an Number of Random Number Cars Arriving of Ranges Cars arrive at a gas station according to the following inter-arrival time distribution. The time to service a car is given by the following service time distribution. Assume the first service begins after the first interarrival time. Interarrival Random Service Time s(in minutes) P(X) Random Numbers 00-29 30-69 70-89 90-99 time (inPCX) minutes) .35 .25 .30 .10 30 5200-34 35-59 60-89 90-99 40 10 20 10 Using the following random number sequence to, estimate the average customer waiting time and the average time a car spends in the system. 5. Average waiting time: 6. Average time in the system:- Service Interarrival 92 15 21 38 74 97 80 64 08 A graduate research assistant "moonlights" at the short order counter in the student union snack bar in the evenings. He is considering asking for help taking orders, but needs to convince the management that they should hire another student. Because he is taking a simulation class, he thinks it may be the perfect way to convince management to hire more help if he can show that customers wait a long time. When a customer arrives, he takes their order and their payment, prepares the food, gives it to the customer, and then takes the order from the next person in line. If someone arrives while he's cooking an order, they must wait until he's completed the current order. He is working on the simulation and a portion is shown below. Assume that order prep time is based on the following distribution: Prep Time Probability 10 .20 .25 .20 15 10 7 7. Complete the following table given that the random numbers for order preptime for customers 3,4, and 5 are 62, 93, and 26, respectively. Time Order Customer Customer Cook Order Prep Receives Wait "Idle" Taken Time Food Time Time Arrival Time of Number Arrival 12 10 8. What is the average customer waiting time? 9. What is the graduate student's utilization? boy sells newspapers and his goal is to maximize profit. He kept a record of his sales for with the following result. His ordering policy is to order an amount each day that is equal to the previous day's demand. A newspaper costs the carrier 50 cents and he sells it for $1.00. Unsold papers are returned and he receives 25 cents (for a loss of 25 cents) Newspapers demand per day of days Number 15 16 17 18 19 20 10 20 42 31 12 10 125 Total 10. Develop the cumulative distribution table and the corresponding random numbers. Newspapers Number of Probability Probability demanded Cumulative Days 10 20 42 31 12 10 per day 15 16 17 18 19 20 Total 11. Use the information and random numbers given in the table below to simulate the sale of newspapers for 10 days. Random aity Sales Demand Papers Day Demand Number Ordered Unsatisfied Unsold 78 43 .93 .87 48 84 87 .27 -20 .52 18 2 10 12. After completing the simulation, determine his total revenue for the ten days 13. After completing the simulation, determine the monetary losses that result from unmet demand and unsold papers.

Answer 1

Sduton Q冂 0、15 0 30 0.25 0-15 0.U5 O 70 0 85 15-44 us-69 70- 84 2 0 15 l-OG 85" S0, domand Valus hlom JJandom numhon R-No 62 13 25 Damand 2 0 R.ND 62 25 uD86 93 Damand 7 5 2