2 The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because ofan anticipated increase in demand, Martin-Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimatedannual fixed cost and the annual capacity for the four proposed plants are as follows:Plant NumberProposed Plant Annual Fixed Cost Annual CapacityDetroit$200,00010,0002Toledo$275,00020,000Denver$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.DistributionCenter NumberDistributionAnnual DemandCenter1.Boston20,0002Atlanta30,0003Houston30,000The shipping cost per unit from each plant to each distribution center is as follows.Distribution CentersPlant Site Boston Atlanta HoustonDetroitToledo44Denver7Kansas City1042St. Louis843 (a) Formulate a mixed-integer programming model that could be used to help Martin-Beck determine which new plant or plants to open in order to satisfy anticipated demand and minimize total cost(in thousands of dollars). (Let x = units shipped in thousands from plant i to distribution center j with the existing plant in St. Louis being plant number 5. Let y, = 1 if a plant is constructed inDetroit and 0 if not, y, = 1 if a plant is constructed in Toledo and 0 if not, y, = 1 if a plant is constructed in Denver and O if not, and y. = 1 if a plant is constructed in Kansas City and O if not.)Mins.t.Detroit CapacityToledo CapacityDenver CapacityKansas City CapacitySt. Louis CapacityBoston DemandAtlanta DemandHouston DemandXy 2 0 for all i and j and y,, y2, Y3, Y4 binary(b) Solve the model you formulated in part (a). What is the optimal cost (in $)?What is the optimal set of plants to open? (Select all that apply.)O DetroitO ToledoO DenverO Kansas City

Given Information: The shipping cost per unit from each plant to each distribution center is as…

Answered: (a) Formulate (in thousands of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 760 homeless patients and no more than 800 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 2,100 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $9,800 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $7,800 per month. How many of each type of patient should it house in order to maximize profit? (If an answer does not exist, enter DNE.) high-income patients homeless patients profit
The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 750 homeless patients and no more than 900 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 1,800 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $9,500 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $8,000 per month. How many of each type of patient should it house in order to maximize profit? HINT [See Example 3.] (If an answer does not exist, enter DNE.) high-income patients: homeless: profit:
The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 700 homeless patients and no more than 620 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 1,800 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $13,000 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $9,000 per month. How many of each type of patient should it house in order to maximize profit? Group of answer choices A)700 homeless patients and 1,100 high-income patients B)1,200 homeless patients and 600 high-income patientsC)700 homeless patients…
Federated Electronics, Ltd., manufactures display screensand monitors for computers and televisions, which it sellsto companies around the world. It wants to construct a new warehouse and distribution center in Asia to serve emerg-ing markets there. It has identified potential sites in the port cities of Shanghai, Singapore, Pusan, Kaohsiung, and HongKong and has estimated the possible revenues for each(minus construction costs which are higher in some citieslike Hong Kong). At each site the projected revenues are primarily based on these factors, (1) the economic condi-tions at the port including the projected traffic, infrastruc-ture, labor rates and availability; and expansion and modernization; and (2) the future government situationwhich includes the political stability, fees, tariffs, duties,and trade regulations. Following is a payoff table thatshows the projected revenues (in $ billions) for six years given the four possible combinations for positive and nega-tive port and…
The Unilever Company plans to allocate some or all of its monthly advertising budget of GH¢82,000 in the Mankato area. It can purchase local radio spots at GH¢120 per spot, local TV spots at GH¢600 per spot, and local newspaper advertising at GH¢220 per insertion.The company's policy requirements specify that the company must spend at least GH¢40,000 on TV and allow monthly newspaper expenditures up to GH¢60,000.The payoff from each advertising medium is a function of the size of its audience. The general experience of the firm is that the values of insertions and spots in terms of "audience points" (arbitrary unit), are as given below: ---------------------------------------------------------------------- Radio 40 audience points per spot TV 180 audience points per spot Newspapers 320 audience points per insertion ---------------------------------------------------------------------
The Bawl Corporation supplies alloy ball bearings to automanufacturers in Detroit. Because of its specialized manu-facturing process, considerable work-in-process and rawmaterials are needed. The current inventory levels are$2,470,000 and $1,566,000, respectively. In addition, fin-ished goods inventory is $1,200,000 and sales (at cost) forthe current year are expected to be about $48 million. Ex-press total inventory asa. Weeks of supplyb. Inventory turns
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If the daily availability of M1 and M2 are 30 tonnes and 12 tonnes respectively in the Reddy Mikks problem, what would be their shadow prices?
Your company presently uses a crew of its own employees for all major maintenance. On average, 40 major repairs are performed each year at 24 lost production hours per repair. Keeping the crew costs $1,000,000 per year plus any lost production cost. Lost production costs are estimated at $2,500 per hour. Your company is considering replacing its in-housemaintenance work with an outside company (Ajax) working under an annual maintenance contract. This proposal will pay Ajax $2,000,000 per year but your company will still have to pay for all lost production time.Ajax claims that the time per repair will decrease because of the contractors’ substantial maintenance experience. Assuming the number of major repairs and the cost of lost production time remain the same, how much time per repair is the maximum allowable for Ajax to be the preferred alternative?
Given that sales volumes are forecast to stay steady at 2,000,000 units, the best option is _________________. 1. Manual Production Line 2. Semi-automatic Production Line 3. Fully Automatic Production Line
b. Five Sales Executives have been told by their company Heavy Machines Limited (HML) that eachsales executive, will be relocated to work at one of five branches of their company, in theCaribbean. The cost to relocate a sales executive at each of the five branches is shown in Table 8below: SalesExecutiveBranchJamaica Antigua/Barbuda Trinidad&TobagoBarbados St. LuciaZenk Murt $2,550 $2,300 $ 2,700 $2,300 $2,400Rangle Tang $2,400 $2,700 $2,800 $2,600 $2,400Atil Heglam $2,600 $2,400 $2,700 $2,500 $2,400Justop Brelim $2,400 $2,500 $3,000 $2,400 $2,500Mesk Lathim $2,400 $2,300 $2,500 $2,800 $2,700 The costs shown in Table 8, are in Eastern Caribbean (EC) dollars. (i) Determine the optimal relocation of the five Sales Executives. Compute and state the total minimum cost.
The water-supply manager for a Midwest city needs to supply the city with at least 10 million gal of potable (drinkable) water per day. The supply may be drawn from the local reservoir or from a pipeline to an adjacent town. The local reservoir has a maximum daily yield of 6 million gallons of potable water, and the pipeline has a maximum daily yield of 10 million gallons. By contract, the pipeline is required to supply a minimum of 6 million gallons/day. If the cost for 1 million gallons of reservoir water is $300 and that for pipeline water is $600, how much water should the manager get from each source to minimize daily water costs, C, for the city?

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