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- A production manager is trying to determine how many units of two types of products to produce each day. One of these is the Standard model, while the other is the Luxurious model. The profit per unit on the Standard model is R600, while the profit per unit on the Luxurious model is R400. The Standard model requires 20 minutes of assembly time, while the Luxurious model requires 35 minutes of assembly time. The Standard model requires 10 minutes of inspection time, while the Luxurious model requires 0.25 hour of inspection time. To meet a specific order, at least 6 Luxurious models must be produced. There are 450 minutes of assembly time and 3 hours of inspection time available each day. Make use of Linear programming graphical method to determine how many units of each product that should be manufactured to maximize profits?7 In a G/G/3 system with average service time equal to 6.9 minutes, average time in system equal to 25.1 minutes, what is the average wait in queue?Maximize 5x+5y subject to 2x+y≤30 x+2y≤24 x,y≥0
- John Swanson, president of Market Research Inc., has asked you to estimate the coefficients of the modelY = β0 + β1X1 + β2X21 + b3X2where Y is the expected sales of office supplies for a large retail distributor of office supplies, X1 is the total disposable income of residents within 5 miles of the store, and X2 is the total number of persons employed in information-based businesses within 5 miles of the store. Recent work by a national consulting firm has concluded that the coefficients in the model must have the following restriction:b1 + b2 = 2Describe how you would estimate the model coefficients using least squares.A company undertakes both construction of new houses and also the repair and renovation of old building. Due to the competition in the market, it has become necessary for the company’s long term plans to obtain a suitable mix of new houses and repair work each year. For planning purpose, the profit on new houses is taken to be 20% of their total value whereas on repair and renovation is 25%. To avoid the problem of having to acquire large amount of land for the building of new houses, the company always plan for at least ¢4,000,000 of repair and renovation work each year but at the same time the company ensures that repairs and renovation do not account for more than half of their total work load. Furthermore, in costing all new and repair work, 5% of the total value of the work load is included to cover the company’s actual fixed overheads which have been estimated at ¢500,000 for the coming year. The other major consideration is the amount of skilled labour which is available. It has…A bus service carries 10 000 people daily between Ajax and Union Station and the company has space to serve up to 15 000 people per day. The cost to ride the bus is $20. Market research shows that if the fare increases by $0.50, 200 fewer people will ride the bus. What fare should be charged to get the maximum revenue, given that the bus company must have at least $130 000 in fares a day to cover operating costs.
- The Organization for Economic Cooperation and Development (OECD) consists of 20 industrialized countries. For these nations, the prediction equation relating y = child poverty rate (in percentage points) to x = social expenditure as a percentage of gross domestic product (GDP) is = 22-1.3x. In 2000, the actual child poverty rate ranged from 2.8% (in Finland) to 21.9% (in the U.S.). Social expenditure as a percentage of GDP ranged from 2% (in the United States) to 16% (in Denmark). What is the residual for the United States? You can use the information on the actual y-value given in the description of the study as well as information from your response to Question 3 to calculate this. Residual for the U.S. =A food manufacturing company wants to hire an auditing firm to asses their food safety performance. Two auditing firms are considered: firm A will change 42$/hr and a flat fee of $4500, while firm B will charge 50$/hr with a flat fee of $3900. What is the break-even point in number of required auditing hours that would yield equal value from both companies?Niue Vanilla has had two successive years in which the Vanilla bean harvest has stretched the firm’s capacity within their drying sheds. Pita, the manger for the drying operation must now make a decision on capacity for next year. Estimated profits under each of the three possible states of nature are as shown in the table below, along with 3 possible alternatives he is considering: Do Nothing, Expand the Drying Shed operation, or Subcontract to a local farmer group who can do some of the drying. Which alternative should be selected if the decision criterion is: Maximax? Maximin?
- A fertilizer producer finds that it can sell its product at a price of p = 300 − 0.1x dollars per unit when it produces x units of fertilizer. The total production cost (in dollars) for x units is C(x) = 15000 − 125x + 0.025x 2 . If the production capacity of the firm is at most 1000 units of fertilizer in a specified time, how many units must be manufactured and sold in that time to maximize the profit?California Wine producer Chill Wines has in their line a mid-market chardonnay, of whichthey produce 200,000 bottles a year. They have been bottling their wines with natural corkclosures, which are known to have sealing issues resulting in the spoilage of wine, aproblem that is worse in their chardonnay than in the other wines they sell. This problem,which results in a 15% spoilage rate for their chardonnay, is both expensive and impactsthe company’s reputation. They have researched several other closure products on themarket and have decided to try using a new closure in a test run of 91 bottles theirchardonnay. After allowing the wine to stay in the bottles for the time it generally takes toget it from the winery to customers, they tested the run and found 16 spoiled bottles. As thecompany has a both an immediate financial and reputation risk, they want to be 90% surethat changing the closures will help limit wine spoilage. What do their results suggest? a)What is known? What…The world price of zinc has increased to the point where “moth balled” zinc mines in east Tennessee have been reopened because of their potential profitability. Solve, (a) What is the estimated annual profit for a mine producing 20,000 tons per year (which is at 100% capacity) when zinc sells for $1.00 per pound? There are variable costs of $20 million at 100% capacity and fixed costs of $17 million per year. (b) If production is only 17,000 tons per year, will the mine be profitable?