Chapter 7, Problem 19QP

The Hills County, Michigan, superintendent of education is responsible for assigning students to the three high schools in his county. He recognizes the need to bus a certain number of students, for several sectors, A - E, of the county are beyond walking distance to a school. The superintendent partitions the county into five geographic sectors as he attempts to establish a plan that will minimize the total number of student miles traveled by bus. He also recognizes that if a student happens to live in a certain sector and is assigned to the high school in that sector, there is no need to bus him because he can walk to school. The three schools are located in sectors B, C, and E. The accompanying table reflects the number of high-school-age students living in each sector and the distance in miles from each sector to each school: Distance to School Sector School in Sector School in Sector School in Sector B C E A B C D E Total 7 0 4 5 12 5 4 0 4 7 6 12 7 7 0 Number of Students 700 500…

A chain of home health care firms in Louisiana needs to locate a central office from which to conduct internal audits and other periodic reviews of its facilities. These facilities are scattered throughout the state, as detailed in the following table. Each site, except for Houma, will be visited three times each year by a team of workers, who will drive from the central office to the site. Houma will be visited five times a year. Q City Covington Donaldsonville Houma Monroe Natchitoches New Iberia Opelousas Ruston Map Coordinates X 750 9.4 7.5 7.8 00 00 4.8 2.8 5.7 4.8 4.0 Y 3N-∞0 60 Nm 0o ∞0 277 00 - 9 N 3.8 N 00 2.2 1.7 8.7 6.8 2.1 3.9 8.2 For the location of the new central office, the coordinates should be near: x = (round your response to two decimal places). b.) y should =____? c.) The center-of-gravity approach minimizes the distance traveled assuming straight lines. This approach ignores geographical features that would tend to violate the straight line constraint such as…

Mansfield Energy Corp has recently taken over a fuel supply plant that is in close proximity to one of its competitors. The collection point for both fuel companies is located at the same seaport. The general manager of Mansfield Energy Corp intends to hire a consultant to train Mansfield Energy Corp’s employees regarding the new procedures for affixing the fuel lines at the collection point to the high-capacity storage tanks and is debating whether the competitor should be invited to attend given that they use the same seaport. The general manager is mindful of the high cost of hiring the consultant and sourcing the equipment to train Mansfield Energy Corp’s employees and is therefore hesitant to invite his competitors. The manager is also aware that there have been no accidents at the port since operations started 10 years ago and might not invite the competitors to participate in the training. The General Manager decides, based on the high price for the consultant (facilitation fee,…

The Janie Gioffre Drapery Company makes three types of draperies at two different locations. At location I, it can make 10 pairs of deluxe drapes, 20 pairs of better drapes, and 13 pairs of standard drapes per day. At location II, it can make 20 pairs of deluxe, 50 pairs of better, and 6 pairs of standard per day. The company has orders for 3000 pairs of deluxe drapes, 6300 pairs of better drapes, and 1800 pairs of standard drapes. If the daily costs are $750 per day at location I and $900 per day at location II, how many days should Janie schedule at each location to fill the orders at minimum cost? location I        days location II        days Find the minimum cost.$

One of Avondale Industries’ global locations (located just outside of London, England) is part of the aircraft wheel and brake production and repair division and focuses on brake repair for aircraft at the nearby Heathrow Airport. The site competes with three other companies in the area to provide brake repair service. Improvements in brake design on several aircraft that the site has service contracts with has necessitated the installation of new equipment to aid the company in responding more quickly and efficiently to service demands. Avondale’s training and development office has been asked to arrange for employee training on the new equipment within one week. What is the most important reason for the employees to be trained quickly to operate the new equipment?     Employees’ skills need to be constantly upgraded for the company to maintain its ability to respond quickly to customer demand.   Employees need to be aware that their jobs could be in jeopardy if they don’t…

A fertilizer manufacturer has to fulfill supply contracts to its two main customers (650 tons to Customer A and 800 tons to Customer B). It can meet this demand by shipping existing inventory from any of its three warehouses. Warehouse 1 has 400 tons of inventory onhand, Warehouse 2 (W2) has 500 tons, and Warehouse 3 (W3) has 600 tons. The company would like to arrange the shipping for the lowest cost possible, where the per-ton transit costs are as follows: W 1 W 2 W 3 $7.50 $6.75 $6.25 $7.00 $6.50 $8.00 Customer A Customer B Write the objective function and the constraint in equations. Let V;= tons shipped to customer i from warehouse j, and so on. For example, VA1 = tons shipped to customer A from warehouse W1. This exercise contains only parts b, c, d, e, and f. b) The objective function for the LP model = Minimize Z = $7.50 + $6.25 + $6.50 (shipping cost to customer A) V + $6.75 + $7.00 + $8.00 (shipping cost to customer B) c) Subject to: Customer A's demand Customer B's demand…

A chain of home health care firms in Louisiana needs to locate a central office from which to conduct internal audits and other periodic reviews of its facilities. These facilities are scattered throughout the state, as detailed in the following table. Each site, except for Houma, will be visited three times each year by a team of workers, who will drive from the central office to the site. Houma will be visited five times a year. City Covington Donaldsonville X= Houma Monroe Natchitoches New Iberia Map Coordinates X 9.4 7.1 7.6 5.2 2.8 5.3 Y 3.2 2.5 Opelousas Ruston For the location of the new central office, the coordinates should be near: 5.2 3.6 1.7 8.1 6.8 2.1 3.3 8.5 y= c.) The center-of-gravity approach minimizes the distance traveled assuming straight lines. This approach ignores geographical features that would tend to violate the straight line constraint such as (select all that apply): A.) Rivers B.) Trips C.) Non-Straight Roads D.) Bridges

Star Garage Limited provides motor vehicle accessories and services for a wide range of vehicles in Dominica. Customers purchase parts to take to their individual mechanics to complete vehicle repairs or they may choose to bring their vehicles to Star Garage for in-house repairs and servicing. This means that they pay for both the parts and the labour associated with the type of service required. Some services do not include any new parts, just the labour costs for that service. Individual customers must pay for all parts purchases in full at the time of sale. Individual customers must pay 50% down when they bring their vehicles in for servicing and pay the balance when they come to pick them up when the job is completed. Corporate customers, however, are billed monthly for all sales (parts or service). Although Star Garage Limited has several different banking accounts, all sales are deposited intact into its main chequing account. Star Garage Limited purchases its inventory of parts…

The MidLands Trucking Company based in Louisvillehas eight trucks located throughout the Mideast that havedelivered their loads and are available for shipments. Through their Internet logistics site MidLands has re-ceived shipping requests from 12 customers. The follow-ing table shows the mileage for a truck to travel to a customer location, pick up the load, and deliver it. Determine the optimal assignment of trucks to customersthat will minimize the total mileage. Customers Truck A B C D E F G H I J K L1 500 730 620 410 550 600 390 480 670 710 440 5902 900 570 820 770 910 660 650 780 840 950 590 6703 630 660 750 540 680 750 810 560 710 1200 490 6504 870 1200 810 670 710 820 1200 630 700 900 540 6205 950 910 740 810 630 590 930 650 840 930 460 5606 1100 860 800 590 570 550 780 610 1300 840 550 7907 610 710 910 550 810 730 910 720 850 760 580 6308 560 690 660 640 720 670 830 690 880 1000 710 680