MAT540 Quantitative Methods Week 3 Homework Complete Solution

Question: #1209

MAT540 Week 3 Homework

Chapter 14

1. The Hoylake Rescue Squad receives an emergency call every 1, 2, 3, 4, 5, or 6 hours, accordingto the following probability distribution. The squad is on duty 24 hours per day, 7 days perweek:
Time Between
Emergency Calls (hr.) Probability
1 0.05
2 0.10
3 0.30
4 0.30
5 0.20
6 0.05
1.00

a. Simulate the emergency calls for 3 days (note that this will require a “running”,orcumulative,hourly clock),using the random number table.
b. Compute the average time between calls and compare this value with the expectedvalue of the time between calls from the probability distribution.Why are the resultsdifferent?

2. The time between arrivals of cars at the Petroco Service Station is defined by the following probability distribution:
Time Between
Arrivals (min.) Probability
1 0.15
2 0.30
3 0.40
4 0.15
1.00

a. Simulate the arrival of cars at the service station for 20 arrivals and compute the averagetime between arrivals.
b. Simulate the arrival of cars at the service station for 1 hour,using a different stream ofrandom numbers from those used in (a) and compute the average time between arrivals.
c. Compare the results obtained in (a) and (b).

3. The Dynaco Manufacturing Company produces a product in a process consisting of operations offive machines. The probability distribution of the number of machines that will break down in a week follows:
Machine Breakdowns
per Week Probability
0 0.10
1 0.10
2 0.20
3 0.25
4 0.30
5 0.05
1.00
a. Simulate the machine breakdowns per week for 20 weeks.
b. Compute the average number of machines that will break down per week.

5. Simulate the decision situation described in Problem 16(a) at the end of Chapter 12 for 20 weeks,and recommend the best decision.
Reference Problem 16(a) in Chapter 12: A concessions manager at the Tech versus A&M football game must decide whether to have thevendors sell sun visors or umbrellas.There is a 30% chance of rain,a 15% chance of overcast skies,and a 55% chance of sunshine, according to the weather forecast in College Junction, where thegame is to be held.The manager estimates that the following profits will result from each decision,given each set of weather conditions:
Weather Conditions
Decision Rain Overcast Sunshine
.30 .15 .55
Sun visors $-500 $-200 $1,500
Umbrellas 2,000 0
-900
a. Compute the expected value for each decision and select the best one.

6. Every time a machine breaks down at the Dynaco Manufacturing Company (Problem 3), either 1,2, or 3 hours are required to fix it, according to the following probability distribution:
Repair Time (hr.) Probability
1 0.30
2 0.50
3 0.20
1.00

a. Simulate the repair time for 20 weeks and then compute the average weekly repair time.