Management science problems | Numerical analysis homework help

Complete the following problems and submit the results in either a Microsoft Word document or a Microsoft Excel spreadsheet. If you choose to use an Excel spreadsheet, place each problem on a separate sheet and label the tab with problem number. Save your document with a descriptive file name, including the assignment and your name.
Chapter 9
Chapter 12
8-1 Bechtold Construction is in the process of installing power lines to a large housing development.  Steve Bechtold wants to minimize the total length of wire used, which will minimize his costs.  The housing development is shown as a network.  Each house has been numbered, and the distances between houses are given in hundreds of feet.   a. What is the required length of power line required? b. What is the recommended route for the lines?
House 7 is currently being demolished and will be removed from the system.
c. With that change, what will be the requirement for power lines and what will the route be?
8-2 The Rockwell Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of 3 per day (approximately Poisson in nature).  The crew can service an average of 8 machines per day, with a repair time distribution that resembles the exponential distribution. a. What is the utilization rate of this service system? b. What is the average downtime for a machine that is broken? c. How many machines are waiting to be serviced at any given time? d. What is the probability that more than one machine is in the system?   e. What is the probability that more than two are broken and waiting to be repaired or being serviced? f. What is the probability that more than three are in the system? g. What is the probability that more than four are in the system?
8-3 Mike Dreskin manages a large Los Angeles movie theater complex called Cinema I, II, III, and IV.  Each of the four auditoriums plays a different film; the schedule is set so that starting times are staggered to avoid the large crowds that would occur if all four movies started at the same time.  The theater has a single ticket booth and a cashier who can maintain an average service rate of 225 movie patrons per hour.  Service times are assumed to follow an exponential distribution.  Arrivals on a typically active day are Poisson distributed and average 210 per hour.  To determine the efficiency of the current ticket operation, Mike wishes to examine several queue operating characteristics. a. Find the average number of moviegoers waiting in line to purchase a ticket. b. What percentage of the time is the cashier busy? c. What is the average time that a customer spends in the system? d. What is the average time spent waiting in line to get to the ticket window? e. What is the probability that there are two or more people in the system? f. What is the probability that there are more than four people in the system? g. What is the probability that there is no one in the system? h. What are two things Mike could to reduce the time to get a ticket?