1. The Football Association of Zambia (FAZ) has four football games on a particular maten day. The Association wants to assign a team of officials to the four games in a way that will minimize the total distance traveled by the officials. The distances in Kilometers for each team of officials to each game location are shown in the table below: Game site Kitwe 160 200 170 120 Ndola Solwezi Lusaka 90 Officials 210 180 70 130 100 175 105 140 D 80 65 105 Find the most efficient assignment using the Hungarian algorithm.
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- Transportation Problems: The EBKK company has three plants producing child push chairs that are to be shipped to four distribution centers. Plans 1, 2, and 3 produce 12, 17, and 11 shipments per month, respectively. Each distribution center needs to receive 10 shipments per month. The distance from each plant to the respective distribution center is given below: DISTRIBUTION CENTER Plant 1 2 3 4 1 800 1300 400 700 2 1100 1400 600 800 3 600 1200 800 900 a. Draw a complete network representation of the problem b. Is the initial solution optimal? c. Find the optimal solution using the MODI Method d. The freight cost for each shipment is $100 plus 50 cents per mile. How much should be shipped from each plant to each of the distribution centers to minimize the total shipping cost?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:…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…
- The Vanguard Publishing Company wants to hire seven of the eight college students who have applied as salespeople to sell encyclopedias during the summer. The company desires to allocate them to three sales territories. Territory 1 requires three salespeople, and territories 2 and 3 require two salespeople each. It is estimated that each salesperson will be able to generate the amounts of dollar sales per day in each of the three territories as given in the following table: Help the company allocate the salespeople to the three territories so that sales will be maximized.KCS Ltd has got three production lines with the same production costs namely; K, L, and S whose production capacities are 140, 160, and 200 units respectively. These are marketed through four destinations B, C, J, and M having demands of 110, 150, 140, and 100 units respectively. The transportation cost between the production lines and market destinations are; K to B, K to C, K to J, K to M, L to B, L to C, L to J, L to M, S to B, S to C, S to J, and S to M as 18, 11, 13, 29, 19, 25, 15, 28, 24, 27, 19, and 12 respectively all costs are US dollars. a).Create a working table taking lines as rows and destinations as columns b). Determine the Cheapest route and Most expensive route to use c).Use the Northwest Corner Method to distribute the products d).Vogel’s Approximation Technique e).Compute their respective total costs incurredA linear programming problem is given as follows:min ? = −4?1 + ?2Subject to 8?1 + 2?2 ≥ 164?1 + 2?2 ≤ 12?1 ≤ 6?2 ≤ 4?1, ?2 ≥ 0 I) Find the A, B, C, D, E, F, and G points on the plot below II) Identify the feasible solution area graphically on the following plot (by shading thearea) III) Which points are the extreme points IV) What is the solution of the optimization problem? (x1=?,x2=?,z=?) Show your work V) Which change will make the problem have multiple optimal solutions? If there is more than one answer, choose all.a) Increase of the coefficient of ?1 on the objective function to 4b) Increase of the coefficient of ?1 on the objective function to 2c) Decrease of the coefficient of ?1 on the objective function to -8d) Increase of the coefficient of ?2 on the objective function to -8e) None VI) If new constraints, ?1≤4 and ?2≤6, are added to the given problem, what effect will be? (choose all the effects)a) The feasible solution area will be smaller.b) The feasible solution area will…
- A Company has 3 production facilities S1, S2 and S3 with production capacity of 7, 9 and 18 units (in 100's) per week of a product, respectively. These units are tobe shipped to 4 warehouses D1, D2, D3 and D4 with requirement of 5,6,7 and 14 units (in 100's) per week, respectively. The transportation costs (in rupees) per unit between factories to warehouses are given in the table below. D1 D2 D3 D4 Capacity S1 19 30 50 10 7 S2 70 30 40 60 9 S3 40 8 70 20 18 Demand 5 8 7 14 34 Find initial basic feasible solution for given problem by usingcolumn minima methodif the object is to minimize the total transportation cost.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?PLEASE SHOW ALL FORMULA 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…
- At the end of a cycle of schedules, a trucking firm has a surplus of one vehicle each in cities A, B, C, D, E, and F and a deficit of one vehicle each in cities 1, 2, 3, 4, 5, and 6. The distances between cities with a surplus and the cities with a deficit are shown below. Find an assignment of surplus vehicles to deficit cities that will result in a minimum total distance. What is the total distance? -Solve the following transportation models using Excel Solver. -Find the optimal solution for the transportation problem having the cost and requirement tablebelow.For the following linear programming problem, determine the optimal solution using the graphical solution method. Max −X + 2Y s.t. 6X − 2Y ≤ 3 −2X + 3Y ≤ 8 X + Y ≤ 3 X, Y ≥ 0 (X, Y) =The Acme Company operates four factories that ship products to five warehouses. The shipping costs, requirements capacities, and optimal allocations are shown below. Factory Shipping Cost per Case to Warehouses Capacity W1 W2 W3 W4 W5 F1 $1.50 $4.50 $6.00 $7.50 $9.00 40,000 30,000 10,000 F2 $3.00 $3.00 $1.50 $6.00 $7.50 30,000 25,000 5,000 F3 $1.50 $7.50 $1.50 $4.50 $1.50 30,000 10,000 20,000 F4 $7.50 $3.00 $6.00 $7.50 $6.00 25,000 25,000 Demand 30,000 35,000 25,000 15,000 20,000 125,000 What is the total cost of the optimal solution? Total cost = $nothing. (Enter your response to the nearest dollar.)