(a) Formulate a mixed-integer programming model that could be used to help Martin-Beck determine which new plant or plants to open in orderto satisfy anticipated demand and minimize total cost (in thousands of dollars). (Let x = units shipped in thousands from plant i todistribution center with the existing plant in St. Louis being plant number 5. Let Y, 1 fa plant is constructed in Detroit and o if not,Y, = 1 if a plant is constructed in Toledo and o if not, y, =1 if a plant is constructed in Denver and o if not, and y, = 1 if a plant isconstructed in Kansas City and O if not.)Mins.t.Detroit CapadityToledo CapacityDenver CapacityKansas City CapacitySt. Louis CapacityBoston DemandAtlanta DemandHouston Demand20 for all i and j and y, y, Y Y, binary(b) Solve the model you formulated in part (a). What is the optimal cost (in s)?What is the optimal set of plants to open? (Select all that apply.)O DetroitO ToledoO DenverD Kansas CityAttanta DemandHouston Demand2o for all i and j and y Y binary(b) Solve the model you formulated in part (a). what is the optimal cost (in s)?What is the optimal set of plants to open? (Select all that apply.)ODetroitO ToledoDenverKansas City(9 Uing equation (13.1),(Sum of varables in the set O) - (sum of varlables in the set 2) (number of variables in the set o) -1where O is the set of binary variatles in our original optimal solution set to one and 2is the set of those set to zero, find a second bestsolution What is the increase in cost (in $) versus the best solution from part (b) The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centerslocated in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing anew plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacityfor the four proposed plants are as follows:Plant NumberProposed PlantAnnual Fixed CostAnnual CapacityDetroit$200,00010,0002.Toledo$325,00020,0003.Denver$350,00030,0004Kansas City$525,00040,000The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows.DistributionDistributionAnnual DemandCenter NumberCenterBoston20,0002.Atlanta30,000Houston30,000The shipping cost per unit from each plant to each distribution center is an follows.Distribution CentersPlant SiteBostonAtlantaHoustonDetroit3Toledo434DenverKansas City104St. Louis3.4.new nlantor nlants to nnen in orderin1,

Answered: The Martin-Beck Company operates a…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Smart Corporation produces and sells laptops. It has four factories and four shops located in different cities. The management of Smart Corporation has just bought a new machine that can improve its productivity. After using the new machine, Smart Corporation's production has increased by 500 units. Therefore, the management has decided to open a new shop and two cities are under their consideration. The two cities under consideration are City E and City F. The shipping cost per unit (RM), factory supplies, and shop demands are as follows Factory Shop Supply A I || IV Demand B 30 40 35 40 с 30 35 50 30 600 700 D E F 45 55 50 45 40 50 35 60 30 45 40 45 55 45 50 55 400 600 500 500 700 800 700 600 1. Determ the best choice of city to open the new shop. Why? 2. Due to the shipping limitation, no unit shall be shipped from I to City B. What would happen to the answer in (a)?
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A flood control reservoir project and channel improvement project are proposed for reducing flood damages along a stream in an urban area. Estimated costs are as follows: Dam and reservoir project Channel improvement project Initial investment $1,500,000 $1,200,000 Annual maintenance $10,000/yr $5,000/yr Hydrologic, hydraulic and economic studies have been conducted to develop the following relationships for the river reach and flood plain: (a) annual exceedance probability versus peak discharge with and without the reservoir, (b) discharge versus stage with and without the channel improvement, and (c) stage versus damage Annual Peak discharge Stage (ft) exceedance (cfs) probability Without With Discharge reservoir reservoir (cfs) Without With Stage Damage project project (ft) million) 0.50 3,000 2,700 0 0 0 9 0.0 0.20 5,400 0.10 7,600 4,200 3,500 5,000 10. 7 10 0.2 10,000 15° 11 15 1.1 0.05 10,400 5,500 15,000 20 14 20 2.2 0.02 0.01 19,000 0.005 24,000 20,000 15,000 8,600 20,000 23 17…
SPANISH AIRPORT Inside the abandoned Spanish airport that cost £1billion to build An airport in Spain has been abandoned for years The Ciudad Real Airport opened in 2008, only for it to close three years later. The Ciudad Real Airport hoped to be an alternative to Madrid Airport. The airport, which was meant to handle overflow from Madrid’s Barajas airport, cost some €1.1 billion to build, including a large amount of public funding for infrastructure. The site is next to a town of just 72,000 people on the sparsely populated Castilian plain and lies more than 140 miles from Madrid. It was even named after Don Quixote, the deluded Castilian gentleman of Cervantes’s famous novel before wiser heads renamed it simply “Central”. Although launched by local private investors, the project has been fully supported by the regional government of Castilla La Mancha and was financed by Caja Castilla La Mancha (CCM), the regional savings bank, or caja. A huge Don Quixote-themed attraction was…

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