In a metropolitan area, 45,000 people want to travel from the city suburbs to the city center. To do so, they can drive, take a city bus, or use the subway system. If x1 number of people drive and x2 number of people take a bus, it will take respectively (0.0006 x1 + 30) and (0.0003 x2 + 40) minutes to make the trip; whereas a subway trip is expected to take 45 minutes. The city bus system can transport a maximum of 20,000 people to the city center, while the subway system has a capacity of transporting at most 10,000. Write a programming formulation that minimizes the average travel time for each person.

In a metropolitan area, 45,000 people want to travel from the city suburbs to the city center. To do so, they can drive, take a city bus, or use the subway system. If x1 number of people drive and x2 number of people take a bus, it will take respectively (0.0006 x1 + 30) and (0.0003 x2 + 40) minutes to make the trip; whereas a subway trip is expected to take 45 minutes. The city bus system can transport a maximum of 20,000 people to the city center, while the subway system has a capacity of transporting at most 10,000. Write a programming formulation that minimizes the average travel time for each person.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter10: Introduction To Simulation Modeling

Section10.6: The Effects Of Input Distributions On Results

Problem 28P

See similar textbooks

Similar questions

In this version of dice blackjack, you toss a single die repeatedly and add up the sum of your dice tosses. Your goal is to come as close as possible to a total of 7 without going over. You may stop at any time. If your total is 8 or more, you lose. If your total is 7 or less, the house then tosses the die repeatedly. The house stops as soon as its total is 4 or more. If the house totals 8 or more, you win. Otherwise, the higher total wins. If there is a tie, the house wins. Consider the following strategies: Keep tossing until your total is 3 or more. Keep tossing until your total is 4 or more. Keep tossing until your total is 5 or more. Keep tossing until your total is 6 or more. Keep tossing until your total is 7 or more. For example, suppose you keep tossing until your total is 4 or more. Here are some examples of how the game might go: You toss a 2 and then a 3 and stop for total of 5. The house tosses a 3 and then a 2. You lose because a tie goes to the house. You toss a 3 and then a 6. You lose. You toss a 6 and stop. The house tosses a 3 and then a 2. You win. You toss a 3 and then a 4 for total of 7. The house tosses a 3 and then a 5. You win. Note that only 4 tosses need to be generated for the house, but more tosses might need to be generated for you, depending on your strategy. Develop a simulation and run it for at least 1000 iterations for each of the strategies listed previously. For each strategy, what are the two values so that you are 95% sure that your probability of winning is between these two values? Which of the five strategies appears to be best?
You now have 10,000, all of which is invested in a sports team. Each year there is a 60% chance that the value of the team will increase by 60% and a 40% chance that the value of the team will decrease by 60%. Estimate the mean and median value of your investment after 50 years. Explain the large difference between the estimated mean and median.
The Decision Sciences Department is trying to determine whether to rent a slow or a fast copier. The department believes that an employee's time is worth $15 per hour. The slow copier rents for $4 per hour, and it takes an employee an average of 10 minutes to complete copying. The fast copier rents for $15 per hour, and it takes an employee an average of six minutes to complete copying. On average, four employees per hour need to use the copying machine. (Assume the copying times and interarrival times to the copying machine are exponentially distributed.) Which machine should the department rent to minimize expected total cost per hour? Worst to slow copier. Better to slow copier. Worst to fast copier. Better to slow copier. A) B) C) D) Answer O A D
The Decision Sciences Department is trying to determine whether to rent a slow or a fast copier. The department believes that an employee's time is worth $15 per hour. The slow copier rents for $4 per hour, and it takes an employee an average of 10 minutes to complete copying. The fast copier rents for $15 per hour, and it takes an employee an average of six minutes to complete copying. On average, four employees per hour need to use the copying machine. (Assume the copying times and interarrival times to the copying machine are exponentially distributed.) Which machine should the department rent to minimize expected total cost per hour? A) B) C) D) Worst to slow copier. Better to slow copier. Worst to fast copier. Better to slow copier. Answer
The Decision Sciences Department is trying to determine whether to rent a slow or a fast copier. The department believes that an employee’s time is worth $15 per hour. The slow copier rents for $4 per hour, and it takes an employee an average of 10 minutes to complete copying. The fast copier rents for $15 per hour, and it takes an employee an average of six minutes to complete copying. On average, four employees per hour need to use the copying machine. (Assume the copying times and interarrival times to the copying machine are exponentially distributed.) Which machine shouldthe department rent to minimize expected total cost per hour?
(Physics: acceleration) Average acceleration is defined as the change of velocity divided by the time taken to make the change, as shown in the following formula: a = (v1 - v0) / t Here, v0 is the starting velocity in meters/second, v1 is the ending velocity in meters/second, and t is the time span in seconds. Assume v0 is 5.6, v1 is 10.5, and t is 0.5, and write the code to display the average acceleration. If you get a logical or runtime error, please refer https://liangpy.pearsoncmg.com/faq.html.
A tire factory wants to set a minimum mileage guarantee on its tyre. Tyre tests reveals that the mean mileage has a normal distribution with mean 128 and standard deviation 1.76. the manufacturer wants to set the minimum guaranteed mileage so that no more than 2.5 percent of tyres will have to be replaced. The Lower limit of guaranteed mileage is :? (Write your answer in 2 decimals places)
Based on Kolesar et al. (1974), Metropolis PD Precinct 88 must determine the minimum number of police cars required to meet its needs for the next 24 hours. An average call for service requires 30minutes. The number of calls the police department expects to receive during each hour is shown in the file P12_61.xlsx. The Metropolis PD standard of service is that there should be a 90% chance that a car is avail-able to respond to a call. For each of the following,discuss how you might find a solution.a. Suppose that patrol officer teams assigned to a car work an 8-hour shift beginning at 12 a.m., 8 a.m., or 4 p.m. Officers get an hour off for a meal. This hour can be anytime between the second and fifthhour of their shift. The precinct wants to know how many teams are needed to meet daily demand.b. Suppose that patrol officer teams assigned to a car begin their 8-hour shifts at 12 a.m., 8 a.m., 12 p.m., 4 p.m., and 8 p.m. An hour off for meals may be taken anytime during a shift. The…
When we consider the time value of money, a peso received in the future: is worth less than a peso received today is worth more than a peso received today is worth the same as a peso received today depends on the compounding used to determine the relationship to a peso received today
Write a program that asks the user for an angle, entered in degrees. The program should then display the sine, cosine, and tangent of the angle. (Use the sin, cos, and tan library functions to determine these values.) You must convert the angle into radians (angle * 3.14/180)
The Decision Sciences Department is tyring to determine whether to rent a slow or fast copier. The department believes that an employee's time is worth $15/hour. The slow copier rents for $4/hr, and it takes an employee an average of 10 minutes to complete copying. The fast copier rents for $15/hr, and it takes an employee an average of 6 minutes to complete copying. On average, four employees per hour need to use the copying machine. (Assume the copying times and interarrival times to the copying machine are exponentially distributed.) Which machine should the department rent to minimize expected total cost per hour? Please note this class revolves around Microsoft Excel so the answer I need needs to show the formulas in Excel, along with any corresponding graphs, etc. Thank you in advance!
The Decision Sciences Department is trying todetermine whether to rent a slow or a fast copier. Thedepartment believes that an employee’s time is worth $15per hour. The slow copier rents for $4 per hour and it takesan employee an average of 10 minutes to complete copying(exponentially distributed). The fast copier rents for $15 perhour and it takes an employee an average of 6 minutes tocomplete copying. An average of 4 employees per hour needto use the copying machine (interarrival times areexponential). Which machine should the department rent?