1. A computer help desk receives new daily customer arrivals according to the following probability distribution: # Arrivals Probability 0 0.05 1 0.2 2 0.3 3 0.2 4 0.15 5 0.1 Random # 01-05 06-25 26-55 56-75 76-90 91-00 The number of customers that the help desk has the capability to serve per day is based on the following probability distribution: # Served 3 4 5 Probability 0.5 0.3 0.2 Random # 01-50 51-80 81-00 If the number of arrivals exceeds the # served capability, the customers will receive top priority the next day. The random numbers drawn for a 5-day simulation are as follows: Arrival Random # 19 34 39 90 97 Service random # 95 95 92 33 85 What will the average number of delays be for the 5-day simulation? 0.9/day 1.2/day None of the alternatives are correct. 0.4/day 2.1/day 2. The demand for refrigerators at an appliance store adheres to the following probability distribution: Demand per day Probability Random # Lead 0 1 2 3 4 Time 1 2 0.15 0.2 0.3 0.2 0.15 0.80 0.20 01-15 16-35 36-65 66-85 86-00 01-80 81-00 The store orders 4 refrigerators per day to have in stock to meet demand. They are trying to maintain low inventory levels. The holding cost is $5/unit/day. The ordering cost is $20 per order. The lost sale cost is $10/unit. A simulation is to be developed to estimate the average daily inventory cost over 5 days. The table below shows the random numbers to be used for refrigerator demand and lead time on orders: day day day day day 1 2 3 4 5 deman d rando m numbe r 88 27 32 36 54 lead time rando m numbe r 54 94 44 75 71 Assuming that beginning inventory is equal to 5 with no prior orders in transit, what is the overall average daily cost of inventory for the 5 days? $32. $53 24 None of the alternatives are correct. $45 3. A certain grocery store has noted the following figures with regard to the number of people who arrive at its three checkout stands ready to check out, and the time it takes to check out the individuals. Arrivals/Mi n. 0 1 2 Frequency 0.3 0.5 0.2 Service Time Frequency in Min 1 0.1 2 0.3 3 0.4 4 0.2 Create an appropriate table of interval of random numbers for both variables. Answer: Arrivals 0 1 2 Interval of Random #s 01-30 31-80 81-00 Service Time Interval of Random #s 1 2 3 4 01-10 11-40 41-80 81-00 The time between arrivals at a drive-through window of a fast-food restaurant follows the distribution given below. The service time distribution is also given in the table below. Use the random numbers provided to simulate the activity of the first five arrivals. Assume that the window opens at 11:00 a.m. and the first arrival after this is based on the first interarrival time generated. Time Between Arrivals 1 2 3 4 Probability Service Time Probability 0.2 0.3 0.3 0.2 1 2 3 0.3 0.5 0.2 Random numbers for arrivals: 14, 74, 27, 03 Random numbers for service times: 88, 32, 36, 24 What times does the fourth customer leave the system? 11:06. None of the alternatives are correct. 11:09 11:04. 11:08. 4. The table below represents the probability distribution for machine breakdowns in a day of operation. Number of breakdowns 0 1 2 3 Probability 0.20 0.30 0.35 0.15 Interval of Random Numbers 1-20 21-50 51-85 86-00 According to the table, if a random number of 00 is drawn, what would the simulated number of breakdowns be? Not enough information provided 2 0 3 1 5. The table below represents the probability distribution for machine breakdowns in a day of operation. Number of breakdowns 0 1 Probability 0.20 0.30 Interval of Random Numbers 1-20 21-50 2 3 0.35 0.15 51-85 86-00 According to the table, what is the probability of at least one breakdown? 0.5 0.8 0.3 0.2 0.85