(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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