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Formulate and prove a sufficient condition for optimality for an infinite-horizon problem.
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- A manufacturing firm plans to expand the current distribution network. The manager of the firm considers whether to extend a long-term contract with the current company who has done business with the firm in the past and whose distribution system reaches 60% of all potential customers. The second option is to sign a one-year contract with a new distribution company. The new company used to reach only 30% of customers, but they claim that they have invested heavily over the past year in distribution resources and now expect to be able to reach 80% of customers. The manager is not that sure about the new company’s claim and give them about 50% of trust. If the new distributor still covers only 30% in year 1, however, the company can switch back to the familiar old distributor. The manager of the firm wants to develop two-scenario plans: 3-year and 10-year planning horizon. Which distributor should the manager choose for each plan? Show your analysis.Problem 1 The Security Company in charge of rescuing visitors in the case of problems at "High Mountain Natural Park" in South Bekaa area has the intention to purchase special trained dogs to help their rescue team, so that they can conduct their search for lost people more efficiently. The rescue team is composed of 10 employees and the company is going to provide each of them with a trained dog. Two types of dogs were selected. The German Shepherd dog breed and the Belgium Malinois breed. The cost of the Belgium Malinois dog breed is $550,00 per dog, while the German Shepherd dog breed is at $850,00 each. For budget reason, the number of German Shepherd dog should be less than half the number of Belgium Malinois. For technical reason, at least three German Shepherd dog must be purchased to get advantage of the special performance of such dog breed in their particular capacity to search for lost person in all weather and under heavy conditions. The overall budget is $6500,00. All of…How did you find the solutions in the table for the range of optimality for the profit coefficient?
- Problem 2 Suppose that for years East Campus' short-run Phillips Curve was such that each 1 percentage point increase in its unemployment rate was associated with a 2-percentage point decline in its inflation rate. Then, during several recent years, the short-run pattern changed such that its inflation rate rose by 3 percentage points for every 1 percentage point drop in its unemployment rate. Graphically, did East Campus' Phillips Curve shift upward or did it shift downward?Place-Plus, a real estate development firm, is considering several alternative development projects. These include building and leasing an office park, purchasing a parcel of land, and building an office building to rent, buying and leasing a warehouse, building a strip mall, and building and selling condominiums. The financial success of these projects depends on interest rate movement in the next 5 years. The various development projects and their 5-year financial return (in €1,000,000s) given that interest rates will decline, remain stable, or increase, are shown in the following image of the payoff table: a) Place-Plus is dissatisfied with the economist’s estimate of the probabilities of future interest rate movement, so it is considering having a financial consulting firm provide a report on future interest rates. The consulting firm can cite a track record which shows that 80% of the time when interest rates declined, it had predicted they would, whereas 10% of the time when…The director of career advising at Grand Valley Commu-nity College wants to use decision analysis to provide in-formation to help students decide which two-year degree program they should pursue. The director has set up the following payoff table for six of the most popular and suc-cessful degree programs at GVCC that shows the estimated five-year gross income ($) from each degree for four futureeconomic conditions:Determine the best degree program in terms of projectedincome, using the following decision criteria:a. Maximaxb. Maximinc. Equal likelihoodd. Hurwicz ( .25) Economic ConditionsDegree Program Recession Average Good RobustGraphic Design 115,000 155,000 190,000 220,000Nursing 140,000 175,000 210,000 225,000Real Estate 95,000 135,000 230,000 350,000Medical Technology 120,000 180,000 210,000 270,000Culinary Technology 85,000 125,000 180,000 290,000Computer InformationTechnology 125,000 160,000 200,000 260,000
- A council has a brown-field sites designated for social housing. After allowing for roads and parks it has an area of 150000 m² for social housing. The housing association intends to build a mixture of flats, two-bedroom houses, three-bedroom houses, and shops (which include a living space) on this site. The housing association wishes to maximise the number of people that can be housed but has strict housing requirements: • there must be at least twice as many two-bedroom houses as three-bedroom houses; • at least 10% of the total housing units excluding shops (i.e. flats and houses) must be flats; • buildings containing the flats (i.e a "block") must have two storeys and every flat must have the same floor space; • shops must be provided at a rate of at least one per 1500 inhabitants. The average number of inhabitants per housing unit and the ground floor area of each are given in the following table. Housing type Flat Two-bedroom house Three-bedroom house Shop Average number of…Monica and Isabel are roommates who, on this particular Saturday morning, are trying to decide what scarf to wear. Each has a Burberry scarf (which we’ll denote B), a tan scarf (denoted T), and a mauve scarf (denoted M). They care about the scarf but also about whether they end up wearing the same or different scarves. The preference ordering (from best to least preferred outcome) for Monica is: (1) she wears B and Isabel wears T or M; (2) she wears T and Isabel wears B or M; (3) she wears B and Isabel wears B; (4) she wears T and Isabel wears T: (5) she wears M and Isabel wears M; and (6) she wears M and Isabel wears B or T. Isabel’s preference ordering is: (1) she wears T and Monica wears B or M; (2) she wears M and Monica wears B or T; (3) she wears T and Monica wears T; (4) she wears M and Monica wears M; (5) she wears B and Monica wears B; and (6) she wears B and Monica wears T or M. Applying the IDSDS, which scarves will be worn?3) A brokerage firm has been tasked with investing $500,000 for a new client. The client has asked that the broker select promising stocks and bonds for investment, subject to the following guidelines: at least 20% in municipal bonds, at least 10% each in real estate and pharmaceutical stock, and at least 40% in a combination of energy and domestic automobile stocks with each accounting for at least 15%. The returns are as follows: Municipal = 5.3%, Domestic Automobile = 8.8%, Energy = 4.9%, Pharmaceuticals = 8.4% and Real Estate = 10.4%. a) Write a linear program complete with objective function and all constraints to Maximize the return. (5 points) b) What is the optimal solution? Give values for all variables rounded to the nearest cent.(2 points) c) How much annual income does the optimal solution generate? (2 points) d) Submit your excel workbook. (2 points)