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Monthly sales of a particular personal computer are expected to decline at the following rate of S'(t) computers per month, where t is time in months and S(t) is the number of computers sold each month. S'(t)= -25t^(2/3) The company plans to stop manufacturing this computer when monthly sales reach 900 computers. If monthly sales now (t=0) are 2,100 computers, find S(t). How long will the company continue to manufacture this computer?
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- Plot the logarithm of arrivals for each transportation mode against time, all on the same graph. Which now appears to be growing the fastest?Q3 Please solve with hand by calculation using formulas (not in excel)When forecasting future sales based on the most recent years's total revenue growing at a revenue growth rate of of 21.85%, with the following years... Year 1 Sales = 209,098,000,000 Year 2 sales = 101,975,000,000 Year 3 sales = 187,879,000,000 Are you calculating it as Year 1 = 209,098 million x .2185 + 209,098,000,000 Year 2 = Year 1 sales answer x .2185 + 101,975,000,000 Year 3 = Year 2 sales answers x .2185 + 187,879,000,000
- Bell Greenhouses has estimated its monthly demand for potting soil to be the following: Assume this trend factor is expected to remain stable in the foreseeable future. The following table contains the monthly seasonal adjustment factors, which have been estimated using actual sales data from the past five years: MONTH ADJUSTMENT FACTOR (%) March +2 June +15 August +10 December −12 a. Forecast Bell Greenhouses’ demand for potting soil in March, June, August, and December 2007. Answer b. If the following table shows the forecasted and actual potting soil sales by Bell Greenhouses for April in five different years, determine the seasonal adjustment factor to be used in making an April 2008 forecast. YEAR FORECAST ACTUAL 2007 500 515 2006 452 438 2005 404 420 2004 356 380 2003 308 320Sally Statistics is implementing a system of statistical process control (SPC) charts in her factory in an effort to reduce the overall cost of scrapped product. The current cost of scrap is $X per month. If a 75% learning curve is expected in the use of the SPC charts to reduce the cost of scrap, what would the percentage reduction in monthly scrap cost be after the charts have been used for 6 months? (Hint: Model each month as a unit of production.)The consumption of electricity in one area has increased historically at 6% per year.If it continues to increase at this rate indefinitely.Find the the number of years before the electricity utility would need to double the amount of generation capacity
- Q4 A business manager determines that t months after production begins on a new product, the number of units produced will be P thousand,where P(t) =6?2 + 5? /(? + 1)2 production in the long run (i) A ruptured pipe in a North Sea oil rig produces a circular oil slick that is y meters thick at a distance x meters from the rupture.Turbulence makes it difficult to directly measure the thickness of the slick at the source (where x = 0),but for x > 0,it is found that y =0.5(x2 + 3x)/ x3 + x2 + 4x Required:a)Assuming the oil slick is continuously distributed,how thick would you expect it to be at the source?In an economics text book, given TSS= 437 and RSS = 291, calculate the ESS and the R-squaredHomeGrown is a small restaurant that specializes in serving local fruits, vegetables, and meats. The company has chosen to enter into a long-term relationship with Family Farms, a local farming operation. The two parties have decided to enter into a long-term contract, where Family Farms will supply produce to HomeGrown at specified prices and volume each year. Before signing a contract, HomeGrown is trying to decide how long the contract should be. It estimates that each year the contract covers saves the restaurant $1,000 in bargaining and opportunism costs. However, each year the contract covers also requires more legal fees. HomeGrown estimates that the number of hours required from lawyers, L, has a quadratic relationship with the number of years on the contract, so that L = Y2, where Y is the number of years for the contract. If HomeGrown’s lawyers charge $100 per hour, how long should the contract be?
- Comfy Limited manufactures glass ornaments and housewares. The business makes use of unskilled labour and providestraining to do hand crafting of the goods. In January, they decided to add a fruit bowl to the range. It took 45.60 hours tocomplete the first two fruit bowls. It was found that labour hours reduced as cumulative output increased, and it is expected thatthis trend will continue until 64 fruit bowls have been manufactured. The total number of hours to complete the next two fruitbowls was 41.04 hours. The labour and material costs to manufacture the first four fruit bowls, which have already been sold,were as follows: Direct materials: R1 360 Direct labour: R1 420Additional information: A gift shop owner saw these fruit bowls and has asked for a quotation for 12 to add to its range of products Since the first four fruit bowls were manufactured, the price of material increased by 8%, and the cost of labour by15%. Comfy Limited paid the designer of the fruit bowl R1 600.…Q6 Suppose that at time t=0, half of a "logistic" population of 100000 persons have heard a certain rumor and that the number of those who have heard it is then increasing at the rate of 500 persons per day. How long will it take for this rumor to spread to 80% of the population? ( Suggestion: Find the value of k by substituting P(0) and P'(0) in the logistic equation) a. About 98 days b. About 34 days c. About 19 days d. About 69 days e. About 119 daysFor arithmetic gradient solutions, the gradient starts _______ periods from Period 0. a N b 0 c 2 d 1