(b) A transport company engaged in carrying parcels has three branches to serve five customers. This distance (km) from each branch to each of the customers is given below: Branches Customers Number of trucks A. D E available 10 12 9. 15 II 4. 4 6. 6. 12 III 15 11 13 8 16 2 Number of trucks required Find out using Vogel's Approximation Method (VAM) the allocation of trucks from branches to customers in order to minimize the total cost of transportation assuming that the cost is proportional to distance. What is the minimum required distance (km) to be run by the trucks? i. ii. iii. If an arrival of a V.V.LP. blocks the traffic from branch II to customers D and E, what should be the optimal allocation in order to minimize the total transportation cost?
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- A company needs to locate three departments (X, Y, and Z) in the three areas (I, II, and III) of a new facility. They want to minimize interdepartmental transportation costs, which are expected to be $.50 per load meter moved. An analyst has prepared the following flow and distance matrices: Distances (meters) Flows (Loads per week) From/To I II III From/To X Y Z I - 10 20 X - 0 80 II - - 10 Y 30 - 150 III - Z 100 130 -If the company were to locate departments X, Y, and Z in areas 1, 2, and 3, respectively, what would be the total distance (in meters) loads would be moved each week?A. 3,100B. 3,600C. 6,200D. 7,200E. 8,200 Work must…BETTER PRODUCTS COMPANY has decided to start manufacturing four new products in three plants that currently have excess production capacity. The products require comparable production effort per unit, so the available production capacity in the plants is measured by the number of units of any product that can be manufactured per day. a)Formulate this problem as a transportation problem by constructing the appropriate parameter table. I already have an optimal solution (it's from the book). (I dont understand)-------------------------------------------------------------------------OPTIMAL SOLUTION:It has basic variables (assignments) X₁₂ = 30, X₁₃ = 30, X₁₅ = 15, X₂₄ = 15, X₂₅ = 60, X₃₁ = 20 and X₃₄ = 25, so that: Plant 1 produces all of products 2 and 3.Plant 2 produces 37.5% of product 4.Plant 3 produces 62.5% of product 4 and all of product 1. The total cost of Z = $3 260 per day.-------------------------------------------------------------------------Instructions:Please explain this…BETTER PRODUCTS COMPANY has decided to start manufacturing four new products in three plants that currently have excess production capacity. The products require comparable production effort per unit, so the available production capacity in the plants is measured by the number of units of any product that can be manufactured per day. a)Formulate this problem as a transportation problem by constructing the appropriate parameter table. I already have an optimal solution (it's from the book). (I dont understand)-------------------------------------------------------------------------OPTIMAL SOLUTION:It has basic variables (assignments) X₁₂ = 30, X₁₃ = 30, X₁₅ = 15, X₂₄ = 15, X₂₅ = 60, X₃₁ = 20 and X₃₄ = 25, so that: Plant 1 produces all of products 2 and 3.Plant 2 produces 37.5% of product 4.Plant 3 produces 62.5% of product 4 and all of product 1. The total cost of Z = $3 260 per day.-------------------------------------------------------------------------Instructions:Please explain this…
- A company needs to locate three departments (I, II, and III) in the three areas (A, B, and C) of a new facility. They want to minimize interdepartmental transportation costs, which are expected to be $.40 per load per meter moved. An analyst has prepared the following distances and flow matrices: Distance (meters) Flows (loads per week) From/To A B C From/To I II III A - 30 40 I - 30 110 B - 60 II 90 - 70 C - III 70 60 - In what areas, A, B, and C, should departments I, II, and III be located that minimize the total cost of moving loads over…Please answer: b) Using a computer software for solving LP, the objective value at the optimal solution Minimum number of total miles traveled (objective value)equals= (round your response to a whole number).Consider the following linear programming model: maximize Z = 3x1 + 2x2 subject to : x1 +x2 ≤ 1 x1 + x2 ≥ 2 x1,x2 ≥ 0 a) Write this model in a standard (augmented) form. (i.e. Introduce slack/surplus, artificial etc.)b) Constract the initial simplex tableau and carry on your calculations to solve this model using the simplex method. Interpret your result.
- QL (“Quebec Lumber”) is a logging and wood processing firm in a remote part of the Canadian province of Quebec. They have recently acquired a remote track of timber that is located ten miles from their processing facility. Normally, this is not a problem as they are able to simply cut the timber and haul it using trucks to their processing facility. However, this track of forestland is ten miles to their north, and there are no roads connecting the tract of land to their facility. They have also acquired a narrow (120 foot wide) ten-mile strip of land connecting this tract of timber to their processing facility. QL considered building their own road between the two points, and have log trucks haul the logs to the processing facility. However, they have decided instead to go with a less expensive option, a narrow gauge railroad. The narrow gauge railroad would require the laying of ties and steel tracks, and will require a custom-built locomotive and rolling stock (train cars that will…The Green Cab Company has a taxi waiting at each offour cabstands in Evanston, Illinois. Four customers have calledand requested service. The distances, in miles, from the waitingtaxis to the customers are given in the following table. Find theoptimal assignment of taxis to customers so as to minimize totaldriving distances to the customers.CAB SITE CUSTOMERABCDStand 1 7348Stand 2 5465Stand 3 6796Stand 4 8674Jim Jones manufactures inexpensive set-it-up-yourself furniture for students. He currently makes two products – bookcases and tables. Each bookcase contributes $24 to profit, and each table, $20. Each product passes through two manufacturing points, cutting and finishing. Bookcases take 4 hours a unit in cutting and 4 hours in finishing. Tables require 3 hours a unit in cutting and 5 in finishing. There are currently 40 hours available in cutting and 50 in finishing. Determine the optimum solution. Use graphic linear programming to find the product mix that produces the maximum profit for Jim.
- Oscar's Bowling, Inc., wants to break into the Phoenix metropolitan market with one of its super-sized 200 lane, 24-hour bowling alleys. It, however, only has enough capital to build one facility. Oscar wants it to be centered by population, as determined by the center of gravity method. The following information is given: City Population x coordinate y coordinate Tempe 275,000 5 5 Scottsdale 415,000 5 10 Chandler 310,000 5 0 Mesa 660,000 10 1 Glendale 335,000 1 10 a. Where should Oscar build? Oscar should build at an x coordinate of nothing and a y coordinate of nothing. b. If Oscar wanted to relocate to the closest city near his new facility, where would he live? (Enter your responses rounded to one decimal place.)Eve started a pizza business three years ago using the kitchen in her house. Customers call to order their pizza and Eve will deliver. Her business has grown so much that she hired four employees. Given the rate of growth, Eve decided to move her operations out of her kitchen and build a separate kitchen for her pizza business. She would like to choose a location that minimizes the total (or average) travel distance to deliver pizza to customers. From historical records, Eve has decided that her customers are unevenly distributed throughout her service area. To make her problem more manageable, she grouped the customers in the same general area into six regions. Using this information and other relevant information obtained from Eve, demonstrate how the centre of gravity location technique can be used to determine the best location that will minimize total travel distance.Eve started a pizza business three years ago using the kitchen in her house. Customers call to order their pizza and Eve will deliver. Her business has grown so much that she hired four employees. Given the rate of growth, Eve decided to move her operations out of her kitchen and build a separate kitchen for her pizza business. She would like to choose a location that minimizes the total (or average) travel distance to deliver pizza to customers. From historical records, Eve has decided that her customers are unevenly distributed throughout her service area. To make her problem more manageable, she grouped the customers in the same general area into six regions. Using this information and other relevant information obtained from Eve, demonstrate how the centre of gravity location technique can be used to determine the best location that will minimize total travel distance b. Using a numerical example, demonstrate how break-even analysis (graphical approach) can be used to determine the…