A bus company believes that it will need the follow- ing numbers of bus drivers during each of the next five years: 60 drivers in year 1; 70 drivers in year 2; 50 drivers in year 3; 65 drivers in year 4; and 75 driv- ers in year 5. At the beginning of each year, the bus company must decide how many drivers to hire or fire. It costs $4000 to hire a driver and $2000 to fire a driver. A driver's salary is $10,000 per year. At the beginning of vear 1 the company has 50 drivers
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![45. A bus company believes that it will need the follow-
ing numbers of bus drivers during each of the next
five years: 60 drivers in year 1; 70 drivers in year 2;
50 drivers in year 3; 65 drivers in year 4; and 75 driv-
ers in year 5. At the beginning of each year, the bus
company must decide how many drivers to hire or
fire. It costs $4000 to hire a driver and $2000 to fire
a driver. A driver's salary is $10,000 per year. At
the beginning of year 1, the company has 50 drivers.
A driver hired at the beginning of a year can be used
to meet the current year's requirements and is paid
full salary for the current year.
a. Determine how to minimize the bus company's sal-
ary, hiring, and firing costs over the next five years.
b. Use SolverTable to determine how the total number
hired, total number fired, and total cost change as
the unit hiring and firing costs each increase by the
same percentage.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F542a0c4e-08a7-4110-84ca-9a91bc31036c%2F2b877cb4-0791-4146-be7a-b8a93cf9e4ec%2Fwu2fqmp_processed.png&w=3840&q=75)
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- During an eight-hour shift, 750 non-defective parts are desired as a result of a manufacturing operation. The default operation time is 15 minutes. As the operators of machine are inexperienced, the actual time they take to perform the operation is 20 minutes, and, on average, a fifth of the parts that start to be manufactured are lost. Assuming that each one of the machines used in this operation will not be available for one hour in each shift, determine the number of machines needed.A machine tool company conducts a job-training programme at a ratio of one for everyten trainees. The training programme lasts for one month. From past experience it has been found thatout of 10 trainees hired, only seven complete the programme successfully. (The unsuccessful traineesare released). Trained machinists are also needed for machining. The company's requirement for thenext three months is as follows:January: 100 machinists, February: 150 machinists and March: 200 machinists.In addition, the company requires 250 trained machinists by April. There are 130 trained machinistsavailable at the beginning of the year. Pay roll cost per month is:Each trainee Rs. 400/- per month.Each trained machinist (machining or teaching): Rs. 700/- p.m.Each trained machinist who is idle: Rs.500/- p.m.(Labour union forbids ousting trained machinists). Build a l.p.p. for produce the minimum costhiring and training schedule and meet the company’s requirement.At a small but growing airport, the local airline company is purchasing a new tractor for a tractor-trailer train to bring luggage to and from the airplanes. A new mechanized luggage system will be installed in 3 years, so the tractor will not be needed after that. However, because it will receive heavy use, so that the running and maintenance costs will increase rapidly as the tractor ages, it may still be more economical to replace the tractor after 1 or 2 years. The following table gives the total net discounted cost associated with purchasing a tractor (purchase price minus trade-in allowance, plus running and maintenance costs) at the end of year i and trading it in at the end of year j (where year O is now). i 012 1 $13,000 j 2 $28,000 $17,000 3 $48,000 $33,000 $20,000 The problem is to determine at what times (if any) the tractor should be replaced to minimize the total cost for the tractors over 3 years. (a) Formulate this problem as a minimum cost flow problem by showing the…
- At a small but growing airport, the local airline company is purchasing a new tractor for a tractor-trailer train to bring luggage to and from the airplanes. A new mechanized luggage system will be installed in 3 years, so the tractor will not be needed after that. However, because it will receive heavy use, so that the running and maintenance costs will increase rapidly as the tractor ages, it may still be more economical to replace the tractor after 1 or 2 years. The following table gives the total net discounted cost associated with purchasing a tractor (purchase price minus trade-in allowance, plus running and maintenance costs) at the end of year i and trading it in at the end of year j (where year O is now). i B 012 1 $13,000 j 2 $28,000 $17,000 3 $48,000 $33,000 $20,000 The problem is to determine at what times (if any) the tractor should be replaced to minimize the total cost for the tractors over 3 years. (a) Formulate this problem as a shortest-path problem by drawing a…Solve the question below using the attached excel templates with formulas for renting both slow and fast copies (labeled in the excel tabs). Question: 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?Solve the question below using the attached excel templates with formulas for renting both slow and fast copies (labeled in the excel tabs). Question: 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?
- establish the significance of random numbers in Monte Carlo simulations.. A group of students organizes a bake sale in which they sell hundreds of cookies at $1per piece. They set up a table on campus and wait for students to come and purchasetheir cookies. Consider the following variables in this bake sale operation:1. Size of the cookies2. Weather conditions on campus3. Organization of the table4. Number of cookies sold5. Competition from other fund-raisers coinciding on campus6. Amount of advertising and shouting of the students at the bake sale table7. Number of students on campus that dayWhich of these variables is an output variable?a. 3b. 4c. 5d. None of the aboveA group of students organizes a bake sale in which they sell hundreds of cookies at$1 per piece. They set up a table on campus and wait for students to come and purchasetheir cookies. Consider the following variables in this bake sale operation:1. Size of the cookies2. Weather conditions on campus3. Organization of the table4. Number of cookies sold5. Competition from other fund-raisers coinciding on campus6. Amount of advertising and shouting of the students at the bake sale table7. Number of students on campus that dayWhich of these variables are input variables?a. 1 and 2b. 1 and 3c. 1, 3, and 5d. 1, 3, and 6
- 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?A large building may require an automated alarm system which monitors and controls all fire and security alarms in the building. Normally, the building is divided into zones and a number of alarms are associated with each zone. Alarms alert a central manned control area who may pass these on to the emergency services or may respond personally.Factors which have to be taken into account in building such a system are:Ø If the control area is unmanned and an alarm is activated this alarm should not be ignored if it is potentially serious. Emergency services should be automatically called.Ø Some but not all parts of the building may be equipped with sprinkler systems or systems to shut down electrical equipment. These should be activated if a fire alarm is confirmed. They should not be activated if there are people in the same room.Ø The building may be equipped with direction indicators which illuminate the route to the nearest exit. These should be activated when a fire alarm is…Chapter 5. (M/M/s/K Model). Leia is responsible for 8 computers in the IT offices in a small business called DataWish. Each computer runs on an average for 3 weeks and requires an average of ½ or 0.5 weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the "arrival" of each computer for service and an exponential distribution to the actual service provided, answer the following questions: a. The arrival rate would bel units per week and the service rate would be units per week. b. Calculate the following operating characteristics for the M/M/s/K system: Utilization Factor (p) Performance Measures c. If we assign a cost of waiting as $500 per week per computer and $800 per week of hiring Leia, what is the Total Time Cost per week cost of servicing the machines? PO (probability that sytem is empty) % dollars L (average units in system) units d. If DataWish decides to hire another individual to help Leia, what would the new Total Time Cost per…
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