If there are decimal points please be as specific as possible and go up to 4 decimal points. Grave City is considering the relocation of several policesubstations to obtain better enforcement in high-crime areas.The locations under consideration together with the areas thatcan be covered from these locations are given in the followingtable:LocationsABCDEFAreas1,4,71,3,5,71,2,52,5,63,4,74,6Areas 2 and 6 must be covered by at least 2 locations. The rest ofthe areas must be covered by at least 1 location.What is the minimum number of locations?

Locations Areas A 1,4,7 B 1,3,5,7 C 1,2,5 D 2,5,6 E 3,4,7 F 4,6

Answered: Grave City is considering the…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section: Chapter Questions

Problem 80P

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Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows: 14, 58, 912, 1316, and 1720. a. Find the optimal investments when at most one investment from each group can be selected. b. Find the optimal investments when at least one investment from each group must be selected. (If the budget isnt large enough to permit this, increase the budget to a larger value.)
A pizza company plans to open new stores in different locations. They consider 6 possible new locations. There are 9 potential areas each location can serve which are listed in the following table. Location Areas Served L1 3,4,8 L2 1,2,5 L3 1,4,7 L4 2,6,9 L5 3,5,9 L6 6,8,7 Each area must be served by at least one location. What is the minimum number of locations?
Transeast Airlines flies planes on the following route:L.A.–Houston–N.Y.–Miami–L.A. The length (in miles) ofeach segment of this trip is as follows: L.A.–Houston, 1,500miles; Houston–N.Y., 1,700 miles; N.Y.–Miami, 1,300miles; Miami–L.A., 2,700 miles. At each stop, the planemay purchase up to 10,000 gallons of fuel. The price of fuelat each city is as follows: L.A., 88¢; Houston, 15¢; N.Y.,$1.05; Miami, 95¢. The plane’s fuel tank can hold at most12,000 gallons. To allow for the possibility of circling overa landing site, we require that the ending fuel level for eachleg of the flight be at least 600 gallons. The number ofgallons used per mile on each leg of the flight is1 (average fuel level on leg of flight/2,000)Review Problems 123To simplify matters, assume that the average fuel level onany leg of the flight isFormulate an LP that can be used to minimize the fuel costincurred in completing the schedule
Carolina Airlines, a small commuter airline in North Carolina, has six flight attendants that it wants to assign to six monthly flight schedules in a way that will minimize the number of nights they will be away from their homes. The numbers of nights each attendant must be away from home with each schedule are given in the following table: Identify the optimal assignments that will minimize the total number of nights the attendants will be away from home.
The Kandy Company wants to schedule the following seven-job problem to be processed on two machines A and B. Each job must be processed by two machines A and B, first on machine A and then machine B. The operation processing times at machine A and Bare as follows: Job i 1 2 3 4 5 6 7 Processing time on Machine A (ai) 9 8 7 12 6 8 15 Processing time on Machine B (bi) 6 5 7 19 12 11 7 a. Suppose jobs arrived in their natural order (i.e., job l before job 2, etc.), and FIFO systems of scheduling and processing the jobs is used. What is the completion time of each job and what is the total throughput time (makespan) of all jobs? b. Suppose the inter-arrival times between jobs can be treated as zero and Johnson’s rule is used to sequence and process the jobs, what is the time of each job and what is the total throughput time (makespan) of all jobs? c. What would be the difference in the average time a job spends in the shop…
The logistic company headquartered in New York wants to expand its business in Chicago, Texas, and Las Vegas. They will place 3 branch heads (A, B a, nd C) from several branch offices owned by the company to set-up offices and run operations in these 3 locations. Below are the costs for allocating the 3 branch heads to each location: Chicago Texas Las Vegas A $8,000,000 $11,000,000 $12,000,000 B $5,000,000 $15,000,000 $13,000,000 C $5,000,000 $10,000,000 $23,000,000 a. Create a table using the assignment method.b. Based on the results of your calculations, what advice can you give to the leader of the company for the most optimum companylocation placement of each of the above branch heads? Explain why?c. What is the total optimum cost that must be incurred by the company to allocate all company branch offices?
The Sav-Us Rental Car Agency has six lots in Nashville, and it wants to have a certain number of cars available at each lot at the beginning of each day for local rental. The agency would like a model it could quickly solve at the end of each day that would tell it how to redistribute the cars among the six lots in the minimum total time. The times required to travel between the six lots are as follows: To (min.) From 1 2 3 4 5 6 1 12 17 18 10 20 2 14 10 19 16 15 3 14 10 12 8 9 4 8 16 14 12 15 5 11 21 16 18 10 6 24 12 9 17 15 The agency would like the following number of cars at each lot at the end of the day. Also, shown is the number of available cars at each lot at the end of a particular day. Determine the optimal reallocation of rental cars. Lot (cars) Cars 1 2 3 4 5 6 Available 37 20 14 26 40 28…
A manufacturer has two factories, located in Toronto and Winnipeg. Warehouses are located in Moncton, Montreal, and Calgary. Minimum requirements at the three warehouses are for at least 5 000, 8 000, and 7 000 units, respectively. The production capacities of the two factories are 9 000 and 11 000 units, respectively. Shipping costs per unit from each factory to each warehouse are given below: WAREHOUSE Moncton Montreal Calgary FACTORY Toronto $14 $6 $18 Winnipeg $22 $17 $9 The manufacturer wants to determine the optimal shipping schedule that will minimize transportation costs. Formulate the linear programming model for this problem.
The distance between two cities in the United States can be approximated by the following formula, where lat1 and long1 are the latitude and longitude of city 1 and lat2 and long2 are the latitude and longitude of city 2. 69 (lat1 − lat2)2 + (long1 − long2)2 Ted's daughter is getting married, and he is inviting relatives from 15 different locations in the United States. The file Wedding gives the longitude, latitude, and number of relatives in each of the 15 locations. Ted would like to find a wedding location that minimizes the demand-weighted distance, where demand is the number of relatives at each location. Assuming that the wedding can occur anywhere, find the latitude and longitude of the optimal location. (Hint: Notice that all longitude values given for this problem are negative. Make sure that you do not check the option for Make Unconstrained Variables Non-Negative in Solver. Round your answers to three decimal places.) latitude of the optimal wedding location:…
Mad Max wants to travel from New York to Dallas bythe shortest possible route. He may travel over the routesshown in Table 8. Unfortunately, the Wicked Witch canblock one road leading out of Atlanta and one road leadingout of Nashville. Mad Max will not know which roads havebeen blocked until he arrives at Atlanta or Nashville. ShouldMad Max start toward Atlanta or Nashville? Which routesshould the Wicked Witch block? Route (Miles)New York–Atlanta 800New York–Nashville 900Nashville–St. Louis 400Nashville–New Orleans 200Atlanta–St. Louis 300Atlanta–New Orleans 600St. Louis–Dallas 500New Orleans–Dallas 300
Instruction: Formulate the dual problems for X2 the following linear programming model No need to compute/doing a tableau 1. Maximize Z = 2X1 + X2 Subject to: X2 < 10 2X1 + 5X2 < 60 X1 + X2 <18 3X1 + X2 < 44 2. Maximize Z = 2X1 + X2 +3X3 Subject X1 + X2 + 2X3 < 400 2X1 + X2 + X3 < 500 3. Maximize Z = 80X1 + 60X2 Subject X1 + X2 = 200 X1 < 50 X2 > 80
CSL is a chain of computer service stores. The number of hours of skilled repair time thatCSL requires during the next five months is as follows:Month 1 (January): 6,000 hoursMonth 2 (February): 7,000 hoursMonth 3 (March): 8,000 hoursMonth 4 (April): 9,500 hoursMonth 5 (May): 11,000 hoursEXAMPLE 1 6 Multiperiod Work Scheduling110 CHAPTER 3 Introduction to Linear ProgrammingAt the beginning of January, 50 skilled technicians work for CSL. Each skilled techniciancan work up to 160 hours per month. To meet future demands, new technicians must betrained. It takes one month to train a new technician. During the month of training, atrainee must be supervised for 50 hours by an experienced technician. Each experiencedtechnician is paid $2,000 a month (even if he or she does not work the full 160 hours).During the month of training, a trainee is paid $1,000 a month. At the end of each month,5% of CSL’s experienced technicians quit to join Plum Computers. Formulate an LPwhose solution will…

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