Pn.09 The Childfair Company has three plants producing child push chairs that are to be shipped to four distribution centers.Plants 1, 2, and 3 produce 12, 17, and 11 shipments per month, respec- tively. Each distribution center needs to receive10 shipments per month. The distance from each plant to the respective distributing centers is given below:DistancePlant12319501250750Distribution Center3550750950Obtain an optimal solution, and determine the total cost.Total Cost = $2145015501350The freight cost for each shipment is $100 plus 50 cents per mile.485011501050

A transportation problem is a type of linear programming problem that involves determining the most…

Answered: The Childfair Company has three plants…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 100P

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A supply chain manager faced with choosing among four possible locations has assessed each location according to the following criteria, where the weights reflect the importance of the criteria. Location Criteria Weight 1 2 3 4 Raw material availability 0.06 P VG OK VG Infrastructute 0.07 P G VG OK Transportation costs 0.33 G P OK P Labor relations 0.25 VG G P OK Quality of life 0.29 G OK P VG VG = Very good 5 pts; G = Good 4 pts; OK = Acceptable 3 pts ; P = Poor 1 pt. Using this information, determine the best and the worst location. Round your answers to two decimal places. Location Total Points 1 2 3 4 ______ is the best location and _______ is the worst location.
a. A farmers' cooperative association plans to build a new sugar mill in Georgetown. The primary objective of the mill is to provide the farmers with a place to take their crop for processing that will reduce their transportation costs. The members of the co-op believe that the center-of-gravity method is appropriate for this objective. While there are over 200 sugar cane farms in the region, they are tightly clustered around six villages. Using the data below, use the center-of-gravity method to calculate the coordinates of the best location for this mill. All mileage references use Browns Town as (0,0). Village Barney Valley Blue Pasture Congo Valley Bower Rabacca Salem Miles East of Miles North of Sugar Cane Browns Town Browns Town 90 140 20 50 100 10 10 60 70 20 80 120 tonnage 240,000 320,000 450,000 120,000 60,000 140,000
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A farmers' cooperative association plans to build a new sugar mill in Georgetown. Theprimary objective of the mill is to provide the farmers with a place to take their crop forprocessing that will reduce their transportation costs. The members of the co-op believe thatthe center-of-gravity method is appropriate for this objective. While there are over 200 sugarcane farms in the region, they are tightly clustered around six villages. Using the data below,use the center-of-gravity method to calculate the coordinates of the best location for this mill.All mileage references use Browns Town as (0,0).VillageMiles East ofBrowns TownMiles North ofBrowns TownSugar CanetonnageBarney Valley 90 10 240,000Blue Pasture 140 60 320,000Congo Valley 20 70 450,000Bower 50 20 120,000Rabacca 100 80 60,000Salem 10 120 140,000
A mattress manufacturer produces mattresses in 5 locations in the North America. The company is planning a new production plant which will supply box springs to all 5 mattress plants. The mattress plants have been located on a coordinate system as follows: Mattress Plant Coordinates (X,Y) A 7,2 В 4,5 5,4 D 6,1 E 8,3 Suppose shipments of box springs to each plant per week were the following: plant A 200 units; plant B 400 units; plant C 300 units; plant D 400 units; plant E 100 units. Which of the following is the closest to the optimal location for the box spring plant? O A. 7.7,4.3 O B. 5.5,3.1 O C. 4.3,7.7 O D. 3.1,4.3 OE. 3.1,5.5
A company that handles hazardous waste wants to minimize the shipping cost for shipments to a disposal center from five receiving stations it operates. Given the locations of the receiving stations and the volumes to be shipped daily, determine the location of the disposal center.
A company has a manufacturing plant that supply three markets in city A, B, and C. Management is looking for a place to locate a single distribution that will minimize total transportation costs. The plant is estimated to move (send) a total of shipment of 12,700 ton per month to the new distribution center. The transportation rate of moving shipment from the plant to the distribution center is $ 0.08 per ton per mile. Market A will receive a total shipment of 6,200 ton per month, market B will receive a total shipment of 2,000 ton per month, and market C will receive a total shipment of 4,500 ton per month. The transportation rate between the distribution center and the markets are as follows: $0.19 per ton per mile to market A, $0.37 per ton per mile to market B, and $0.25 per ton per mile to market C. The horizontal and vertical coordinates of the plants and markets are follows: Plant, 25, 75 Market A, 30, 5 Market B, 36, 24 Market C, 15, 40 Use the Center-of-Gravity method to find…
(A) Determine the total number of future trips generated in all zone? This table shows Number of currant Household and currant trips Zone A Zone B Zone C No. of No. of No. of person/Household = person/Household = person/Household = Auto/ Household 1 2-3 >3 No. of No. of No. of No. of No. of No. of Н.Н trips Н.Н trips Н.Н trips 1100 220 1500 600 1800 1080 1 950 380 1200 600 120 90 >1 80 100 200 300 50 80 This table shows Number of future Household Zone A Zone B Zone CTH No. of No. of No. of Auto/ Household person/Household = person/Household = person/Household 1 2-3 >3 3000 5000 6000 1 1500 4000 800 >1 300 700 200
I have two locations where I will be delivering goods. Vaalbara is located at coordinates (10,0) and I have 10 truckloads going to it. Kenorland is located at coordinates (20,20) and I have 40 truckloads going to it. What is the center of gravity's X coordinate? Round to the nearest whole number (e.g. 33.2 -> 33). I have two locations where I will be delivering goods. Vaalbara is located at coordinates (10,0) and I have 10 truckloads going to it. Kenorland is located at coordinates (20,20) and I have 40 truckloads going to it. What is the center of gravity's Y coordinate? Round to the nearest whole number (e.g. 33.2 -> 33). 0*10 + 20*40 = 800. Sum of loads = 50. Y coordinate = 16
Required information The Childfair Company has three plants producing child push chairs that are to be shipped to four distribution centers. Plants 1, 2, and 3 produce 12, 17, and 11 shipments per month, respec- tively. Each distribution center heeds to receive 10 shipments per month. The distance from each plant to the respective distributing centers is given below: Distance Plant 1 2 3 1 1450 1750 1250 Distribution Center 3 1050 1250 1450 Obtain an optimal solution, and determine the total cost. Total Cost = $ 2 1950 2050 1850 The freight cost for each shipment is $100 plus 50 cents per mile. 4 1350 1650 1550
A company that handles hazardous waste wants to minimize the shipping cost for shipments to a disposal center from five receiving stations it operates. The locations of the receiving stations and the volumes to be shipped daily are given in the below table: Location ( x, y ) Daily Volume ( in truck loads ) A (5.70,5.00) 15 B (4.00,7.70 ) 9 C (1.90,2.80 ) 18 D (2.10,5.20 ) 16 E (7.50, 6.30) 17 1. Which one of the following coordinate is closest to the optimal location using median method? a) (4.00,5.20) b) (4.00,3.64) c) (2.60,5.20) d) (5.80,3.12) 2. Which one of the following coordinate is closest to the optimal location using gravity method? a) (4.22,4.62) b) (5.91,6.16) c) (4.22,5.13) d) (5.28,5.13) 3. Which one of the following is closest to the total distance traveled (optimal objective function value) using Rectilinear distance measure for the optimal median solution? a) 241 b)352 c)157 d)133
7. The BD restaurant chain purchases materials from four different food suppliers. The company wants to construct a new central distribution center to process and package the materials before shipping them to their various restaurants. The suppliers transport items in 40-foot truck trailers, each with a capacity of 38,000 lbs. The locations of the four suppliers and the annual number of trailer loads that will be transported to the distribution center are shown in the following table (distance in miles). Using the center-of-gravity method, determine a possible location for the distribution center. A B с D X Y 200 200 100 500 250 600 500 300 Load 75 105 135 60 BD wants to evaluate three different sites it has identified for its new distribution center relative to the four suppliers identified. The coordinates of the three sites under consideration are as follows: Site 1: x1 = 360, y₁ = 180 Site 2: X2 = 420, y2 = 450 Site 3: X3 = 250, y3 = 400

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