Magnus Packard is an underwriter who works at Capital State Financial where he processes loans daily. He usually takes an average of 40 minutes to process each loan or job and can identify how long each one will take based on a few key indicators within the application. Today, he has five loans that he must process by the end of the day. Each job is labeled in alphabetical order based on the order in which it arrived. For example, A arrived first, and B came in second, etc. (See table below) Job Processing Time (minutes) SPT? A 50 A) A, B, C, D, E, F B) E, D, F, B, A, C B C 40 Q2. Let's say, Magnus' office requires underwriters to follow the shortest- processing-time (SPT) rule. In what order will Magnus complete the jobs with D E F 60 30 25 35 C) C, D, E on Day 1 and A, B, F on Day 2 D) D, E, F on Day 1 and A, B, C on Day 2 E) C, A, B, F, D, E come-
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- Winkler Furniture manufactures two different types of china cabinets: a French Provincial model and a Danish Modern model. Each cabinet produced must go through three departments: carpentry, painting, and finishing. The table on this page contains all relevant information concerning production times per cabinet produced and production capacities for each operation per day, along with net revenue per unit produced. The firm has a contract with an Indiana distributor to produce a minimum of 300 of each cabinet per week (or 60 cabinets per day). Owner Bob Winkler would like to determine a product mix to maximize his daily revenue.Use Solver to solve the problem. You need to have one Excel sheet with the problem setup and another sheet with Solver solutionThe Enormous State University History Department offers three courses- Ancient, Medieval and Modern History- And the chairperson is trying to decide how many sections of each to offer this semester. The department is allowed to offer 43 sections total, there are 4,700 students who would like to take a course, and there are 56 professors to teach them. Sections of Ancient History have 100 students each, sections of Medieval History hold 50 studennts each, and sections of Modern History have 200 students each. Modern History sections are taught by a team of two professors, while Ancient and Medieval History need only one professor per section. How many sections of each course should the chair schedule in order to offer al the sections that they are allowed, accomodate all the students, and give one teaching assignment to each professor? HINT [See example 2.] (Assume each section has the maximum number of students allowed.) Ancient History = Sections Medieval History…Chaka Furniture Shop located in Cavite makes two kinds of products, cabinets and dressers, which pass through the assembly and the finishing departments. The Assembly department has 48 hours of work available each week, while the finishing department has 36 hours each week. Making one cabinet needs 3 hours in Finishing and 2 hours in Assembly, while it takes 3 hours to assemble a dresser and 4 hours to finish it. a.) If the profit generated per cabinet is ₱80 and per dresser is ₱100, write the objective function that best describe the given problem where x is the number of cabinet produced, y is the number of dresser produced and P is the profit. b.) How many units of dresser should the company produce to maximize the profit? c.) How many units of cabinet should the company produce to maximize the profit? d.) What is the maximum profit for the given problem?
- At a machine tool plant, five jobs must be completedeach day. The time it takes to do each job depends on themachine used to do the job. If a machine is used at all, thereis a setup time required. The relevant times are given inTable 20. The company’s goal is to minimize the sum of thesetup and machine operation times needed to complete alljobs. Formulate and solve (with LINDO, LINGO, or ExcelSolver) an IP whose solution will do this. Machine 1 2 3 4 5 Time (Minutes)1 42 70 93 X X 302 X 85 45 X X 403 58 X X 37 X 504 58 X 55 X 38 605 X 60 X 54 X 20A small metal-parts shop contains three machines—a drillpress, a lathe, and a grinder—and has three operators, eachcertified to work on all three machines. However, each op-erator performs better on some machines than on others.The shop has contracted to do a big job that requires allthree machines. The times required by the various opera-tors to perform the required operations on each machineare summarized as follows:The shop manager wants to assign one operator to eachmachine so that the total operating time for all three opera-tors is minimized. Formulate and solve a linear program-ming model for this problem.Mazy's Department Store has decided to stay open for business on a 24-hour basis. The store manager has divided the 24-hour day into six 4-hour periods and has determined the following minimum personnel requirements for each period: Time Personnel Needed Midnight4:00 A.M. 90 4:008:00 A.M. 215 8:00 A.M.Noon 250 Noon4:00 P.M. 65 4:008:00 P.M. 300 8:00 P.M.Midnight 125 Store personnel must report to work at the beginning of one of these time periods and must work for 8 consecutive hours. The store manager wants to know the minimum number of employees to assign to each 4-hour segment to minimize the total number of employees. Formulate and solve this problem.
- 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 schedulea company possesses two manufacturing plants, each of which can produce three products: X,Y, and Z from common raw material. However, the proportions in which the products are produced are different in each plant and so are the plant’s operating costs per hour. Following are the data on the production per hour and costs together with current orders in hand for each product. a company possesses two manufacturing plants, each of which can produce three products: X,Y, and Z from common raw material. However, the proportions in which the products are produced are different in each plant and so are the plant’s operating costs per hour. Following are the data on the production per hour and costs together with current orders in hand for each product. Plant product operating cost per hour(birr) X YZ A 2 4 3 9 B 4 3 2 10 Orders on hand 54 24 60 You are required to use graphical method to find out the number of production hours needed to fulfill the orders on…hapter 9. TechConsult Projects Ltd provides technical services to various small businesses in the San Antonio area. They have four technicians available to schedule and Tech1 can work for 160 hours, Tech2 can work for 110 hours, Tech3 can work for 160 hours, and Tech4 can work for 130 hours in the next month. Four clients are seeking technical services from the company and each of them requires 140 hours of technical support in the next month. The billing rates for the technicians are based on the type of work each client project requires and the skills they have. The rates in dollars per hour are as follows. Based on the E-clips example from the textbook, you can see that this is an assignment problem because the goal of TechConsult is to maximize their billing for the month. Create a network, a linear program, and find the optimal values of the hours that each technician should be assigned for each client and answer the questions below the table (it is okay to round to whole numbers…
- Airline Scheduling. Alpha Airline wishes to schedule no more than one flight out of a given airport to each of the following cities: C, D, L, and N. The available departure slots are 8 a.m., 10 a.m., and 12 noon. Alpha leases the airplanes at the cost of $5000 before and including 10 a.m. and $3000 after 10 a.m., and is able to lease at most two per departure slot. Also, if a flight leaves for location N in a time slot, there must be a flight leaving for location L in the same time slot. The expected profit (in $1000) contribution before rental costs per flight is shown in the table below. Time Slot 8 10 12 C 10 6 6 D 9 10 9 L 14 11 10 N 18 15 10 a) Formulate an integer linear program model that can be used to find the profit-maximizing schedule. Define your decision variables as Xij = 1 if a flight to destination i occurs in time slot j and Xij = 0 otherwise; and Yj = number of airplanes rented for time slot j. Write the objective function and all the constraints. b)…A company has three manufacturing plants (in Atlanta,Tulsa, and Springfi eld) that produce a product that is then shipped to one of four distribution centers. Th e three plants can produce13, 18, and 12 truckloads of product each week, respectively. Eachdistribution center needs 10 truckloads of product each week. Th eshipping costs per truckload between the plants and distributioncenters are given in the table. Th e company needs to determinehow much to ship from each plant to each distribution center andwould like to minimize total shipping costs (a) Formulate an LP to minimize the total shipping costs.(b) Set up and solve the problem on a spreadsheet.(c) What is the optimal solution? Explain the rationale for thesolution