Quantitative Analysis

I have some Quantitative Analysis questions I need help understanding.

Simulation Modeling

1. A certain grocery store has noted the following figures with regard to the number of people who arrive at their three checkout stands ready to check out and the time it takes to check out the individuals.

Arrivals/Min. Frequency Service Time in Min. Frequency
0 0.3 1 0.1
1 0.5 2 0.3
2 0.2 3 0.4
4 0.2

Simulate the utilization rate of the three checkout stands over four minutes using the following random numbers for arrivals: 07, 60, 49, and 95. Use the following random numbers for service: 77,76, 51, and 16. Note the results at the end of the 4 minute period.

2. The number of machine breakdowns in a day is 0, 1, or 2, with probabilities 0.6, 0.3, and 0.1, respectively. The following random numbers have been generated: 13, 10, 02, 18, 31, 19, 32, 85, 31, 94. Use these numbers to generate the number of breakdowns for 10 consecutive days. What proportion of these days had at least 1 breakdown?

3. Average daily sales of a product are 8 units. The actual number of sales each day is either 7, 8, or 9, with probabilities 0.3, 0.4, and 0.3, respectively. The lead time for delivery of this averages 4 days, although the time may be 3, 4, or 5 days, with probabilities 0.2, 0.6, and 0.2. The company plans to place an order when the inventory level drops to 32 units (based on the average demand and average lead time). The following random numbers have been generated: 60, 87, 46, 63 (set 1) and 52, 78, 13, 06, 99, 98, 80, 09, 67, 89, 45 (set 2). Use set 1 of these to generate lead times and use set 2 to simulate daily demand. Simulate 2 ordering periods with this and determine how often the company runs out of stock before the shipment arrives.

4. 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 AM and the first arrival after this is based on the first interarrival time generated.

Time Between Service
Arrivals Probability Time Probability
1 0.2 1 0.3
2 0.3 2 0.5
3 0.3 3 0.2
4 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?