1. The approximate travel time for officiating crews for college basketball for four games scheduled for a weekend are shown in the following table: Game Site Crew Syracuse Buffalo Rochester Ithaca A 1.2 1.4 0.2 1.5 B 1.0 2.0 0.5 1.0 C 1.2 3.4 2.4 0.5 D 2.1 3.1 1.1 0.8 NOTE: Time in hours Use Excel to answer the following questions: What set of crew assignments will minimize travel time What is the total time required for the optimal assignment
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- Answer the following questions after reviewing the problem. 4. Problem 5.17: American Football. The offensive coordinator for the Chicago Bears professional football team is preparing a game plan for the upcoming game against the Green Bay Packers. A review of game tapes from previous Bears–Packers games provides data on the yardage gained for run plays and pass plays. Data shows that when the Bears run against the Packers’ run defense, the Bears gain an average of 2 yards. However, when the Bears run against the Packers’ pass defense, the Bears gain an average of 6 yards. A similar analysis of pass plays reveals that if the Bears pass against the Packers’ run defense, the Bears gain an average of 11 yards. However, if the Bears pass against the Packers’ pass defense, the Bears average a loss of 1 yard. This loss, or negative gain of −1, includes the lost yardage due to quarterback sacks and interceptions. Develop a payoff table that shows the Bears’ average yardage gain for each…Grave City is considering the relocation of several police substations to obtain better enforcement in high-crime areas. The locations under consideration together with the areas that can be covered from these locations are given in the following table: Potential Locationsfor Substations Areas Covered A 1, 5, 7 B 1, 2, 5, 7 C 1, 3, 5 D 2, 4, 5 E 3, 4, 6 F 4, 5, 6 G 1, 5, 6, 7 Formulate an integer programming model that could be used to find the minimum number of locations necessary to provide coverage to all areas.Consider the following linear program. Max 1A + 2B s.t 1A≤ 4 1B≤ 3 2A + 2B = 10 A, B ≥ 0 (a) Show the feasible region. (b) What are the extreme points of the feasible region? (b) What are the extreme points of the feasible region? smaller x-value (A, B) = (______) larger x-value (A,B)= (_____) (c) Find the optimal solution using the graphical procedure. (A, B) = (______)
- Mitch just built 4 franchise locations for his newest pizzerias and wants to decide where to put his headquarters. He makes 1 weekly visit to his Northside store (X = 3, Y = 10), 2 visits to his Eastside store (X = 4, Y = 6), 3 visits to his Southside store (X = 2, Y = 5) & 4 visits to his Westside store (X = 1, Y = 4). __________ 1. Using the store visits as weights, compute the coordinates of the center of gravity to help him with his location decision.The JPC Company has five different production jobs to complete next week. Five multipurpose machines, each with somewhat different characteristics are available. The estimated costs of completing each job on each of the five machines are as follows: Allocate each job to each machine for minimum cost: Job 2 was assigned to? what is total assignment cost?The Palestinian ministry of sports has four basketball games on a particular night. The ministry wants to assign four teams of officials to the four games in a way that will minimize the total distance traveled by the officials. The supply is always one team of officials and the demand is for only one team of officials at each game. The distances in km for each team of officials to each game location are shown in the following table officials 1 2 3 a 100 150 120 b 130 210 90 c 120 170 90 A) Formulate this problem as Assignment Model (the objective function and constraint equations for the demand and supply) . b) Use QM to solve the Model.
- A rapidly expanding company is looking to lease a small plant in Memphis, Tennessee, Biloxi, Mississippi, or Birmingham, Alabama. Prepare a cost benefit study for each of the three locations using the following data: The annual construction, facilities, and administration expenses for Memphis, Biloxi, and Birmingham will be $40,000, $60,000, and $100,000, respectively. In Memphis, labour and materials are estimated to cost $8 per month, $4 in Biloxi, and $5 in Birmingham. The Memphis site would add $50,000 a year to device transportation expenses, the Biloxi location would add $60,000 per year, and the Birmingham location would add $25,000 per year. The annual production is expected to be 10,000 units.J 2 An electronics store wants to identify a location for a warehouse that will ship to five retail stores. The coordinates and annual number of truckloads are given in the accompanying table. Develop a model to find the best location, assuming that straight-line distances can be used between the locations. Experiment with the model by testing each of the possible best solutions, included, to find the best location. Click here to view the data for the store locations and annual numbers of truckloads. Click here to view some possible best solutions. The best location is at____. (Type an ordered pair. Round each coordinate to the nearest integer as needed.)Consider the following linear program. Max 2A + 3B s.t. 5A + 5B ≤ 350 Constraint 1 −1A + 1B ≤ 10 Constraint 2 1A + 3B ≥ 90 Constraint 3 A, B ≥ 0 Identify the optimal extreme point. What is the optimal solution? (A, B)= (30, 40) How much slack or surplus is associated with the nonbinding constraint? Constraint 3 is the nonbinding constraint. There is a surplus of _________ associated with this constraint. (THE QUESTION BEING ASKED)
- Grave City is considering the relocation of several police substations to obtain better enforcement in high-crime areas. The locations under consideration together with the areas that can be covered from these locations are given in the following table: 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 Areas 2 and 6 must be covered by at least 2 locations. The rest of the areas must be covered by at least 1 location. What is the minimum number of locations?The north-south highway system passing through Albany, New York can accommodate the capacities shown in the table below. From To Capacities 1 2 3 1 3 6 1 4 3 2 4 2 2 5 4 3 4 3 3 6 2 4 2 2 4 3 3 4 5 2 4 6 3 5 2 4 5 4 2 5 6 6 How many units go from Node 1 to 3 and 4 to 2, respectively, in order to maximize the flow. a. 5 and 1. b. 5 and 2. c. none of the answers proposed apply d. 6 and 1. e. 6 and 2.Two law students, John and Marsha, are planning an all-nighter to prepare for theirlaw boards the following day. Between them they have one set of materials in thefollowing five subjects: contracts, torts, civil law, corporate law, and patents.Based on their previous experience, they estimate that they will need the following amount of time (in hours) with each set of materials:Contracts Torts Civil Corporate PatentsJohn 1.2 2.2 0.7 0.5 1.5Marsha 1.8 0.8 3.1 1.1 2.3They agree that Marsha will get the opportunity to see each set of notes beforeJohn. Assume that they start their studying at 8:00 P.M. Determine the exact timesthat each will begin and end studying each subject in order to minimize the totaltime required for both to complete studying all five subjects