The Green Cab Company has a taxi waiting at each of four cabstands in Evanston, Illinois. Four customers have called and requested service. The distances, in miles, from the waiting taxis to the customers are given in the following table. Cab Site Stand 1 Stand 2 Stand 3 Stand 4 The optimal assignment of taxis to customers that minimizes the distance is: A 5 3 4 6 B 1 2 5 4 → Customer Stand 3 Stand 2 Stand 1 Stand 4 C 2 4 7 5 Customer A Customer B Customer C Customer D The cumulative distance of the optimal assignment of taxis to customers = miles (enter your response as a whole number). D 6 3 4 2
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- solve with excel solver PharmaCo wants to determine how to deploy sales representatives across its Western U.S. region to support a new drug for obesity. Sales representatives will be located in a "home city", which they serve, in addition to cities with feasible commuting distance, with the objective that all cities must be served by at least one sales representative. The feasible connections between each city in the region are listed below (1 indicates a feasible connection, potential home cities are shown in columns, and cities served in rows): Potential Rep Home City Served? Albuquerque El Paso Denver Phoenix San Diego Los Angeles San Francisco Portland Seattle Las Vegas Salt Lake City Albuquerque 1 1 1 1 0 0 0 0 0 0 0 El Paso 1 1 0 1 0 0 0 0 0 0 0 Denver 1 0 1 1 0 0 0 0 0 0 1 Phoenix 1 1 1 1 1 1 0 0 0 1 1 San Diego 0 0 0 1 1 1…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:…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.
- Solve using the duality linear programming method of the following problem:Object Function: F = X1+X2+4X3Subjected to:X1+2X2+3X3 ≥ 1152X1+X2+8X3 ≥ 200X1+X3 ≥ 50X1,X2, X3 ≥ 0 Note: Please make sure to use the duality linear programming method.Brooks City has three consolidated high schools, each with a capacity of 1,200 students. The school board has partitioned the city into five busing districtsnorth, south, east, west, and centraleach with different high school student populations. The three schools are located in the central, west, and south districts. Some students must be bused outside their districts, and the school board wants to minimize the total bus distance traveled by these students. The average distances from each district to the three schools and the total student population in each district are as follows: The school board wants to determine the number of students to bus from each district to each school to minimize the total busing miles traveled. a. Formulate a linear programming model for this problem. b. Solve the model by using the computer.Brooks City has three consolidated high schools, each with a capacity of 1,200 students. The school board has partitioned the city into five busing districts—north, south, east, west, and central—each with different high school student populations. The three schools are located in the central, west, and south districts. Some students must be bused outside their districts, and the school board wants to minimize the total bus distance traveled by these students. The average distances from each district to the three schools and the total student population in each district are as follows:Distance (miles)DistrictCentral SchoolWest SchoolSouth SchoolStudent PopulationNorth 8 11 14 700South 12 9 — 300East 9 16 10 900West 8 — 9 600Central — 8 12 500The school board wants to determine the number of students to bus from each district to each school to minimize the total busing miles traveled.a. Formulate a linear programming model for this problem and solve the model using the computer.b. The…
- A manufacturing company produces two types of products called X and Y. Each product uses four different machines like lathe, drilling, grinding & milling operations. The profit per unit of selling X and Y are 7 RO and 3 RO respectively. Formulate a linear programming model with the given constraints to determine the production volume of each product in order to maximize the total profit (in OR). Solve the following linear programming model by using Graphical method. Subject to, 6X + 4Y ≤ 24 X + 2Y ≤ 6 -X + Y ≤ 1 Y ≤ 2 and X,Y ≥ 0Solve the following problems using Excel Solver or R Studio. A company produces cars in Atlanta, Boston, Chicago, and Los Angeles. The cars are then shipped to warehouses in Memphis,Milwaukee, New York City, Denver, and San Francisco. The number of cars available at each plant is given in Table 1. Eachwarehouse needs to have available the number of cars given in Table 2. The distance (in miles) between the cities is given inTable 3. Assuming that the cost (in dollars) of shipping a car equals the distance between two cities, determine an optimalshipping schedule.The Sunshine Rental Car Agency has six lots in Orlando,and it wants to have a certain number of cars available ateach lot at the beginning of each day for local rental. Theagency would like a model it could quickly solve atthe end of each day that would tell how to redistribute thecars among the six lots at the minimum total mileage.The distances between the six lots are as follows:
- The Smart Fertilizer Company produces two types of soil, Fastgro and Nergy. The company has developed the following non-linear optimization model to determine the optimal number of bags of Fastgro (x1) and Nergy (x2) that it must produce each day to maximize profit, given the constraint for available clay. Determine the optimal number of Fastgro and Nergy bags to create to maximize profit. max Profit($) = 30x1 −2x21 + 25x2 −0.5x22subject to 3x1 + 6x2 = 300x1, x2 ≥0x1, x2 integerThe network below shows the flows possible between pairs of six locations. A graph with 6 nodes and 13 directed arcs is shown. Node 1 is connected to node 2 by arc of value 17, to node 3 by arc of value 19, and to node 5 by arc of value 9. Node 2 is connected to node 3 by arc of value 8 and to node 4 by arc of value 14. Node 3 is connected to node 2 by arc of value 5, to node 4 by arc of value 9, to node 5 by arc of value 7, and to node 6 by arc of value 24. Node 4 is connected to node 3 by arc of value 9 and to node 6 by arc of value 13. Node 5 is connected to node 3 by arc of value 7 and to node 6 by arc of value 11. Node 6 has no directed arcs directed to other nodes. Formulate an LP to find the maximal flow possible from node 1 to node 6. (Let xij represent the flow from node i to node j. Enter your maximum flows as a comma-separated list of inequalities.) Max s.t.Node 1 Flows Node 2 Flows Node 3 Flows Node 4 Flows Node 5 Flows Node 6 Flows…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