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- Redleaf company's market research department works on the manufacture and marketing of a winter tire for vehicles. Currently the price is 10$, and the demand is 13000 units. When the price is increased to 15$, the company expects the demand to be 8500 units (assume that price is linearly related to demand.). Company is following a make-to-order policy for their production, meaning that they make production as much as ordered from their dealers. The dealers make orders 3 times a year, on January, May and September. The company has 23 dealers, who do not have any capacity restriction on their orders. Yet, the above information is a country-wise research, and shows the aggregate demand (sum of all dealers' orders) for each price. Regardless of the production amount, the company faces with a 2170$ of administrative cost for production, in addition to 1,3 $ cost of raw materials and labour costs per each units produced. If we define price as a function of demand (P(d)) using the…A herbal tea producer company has 24 different products in the market, each are produced in one of the 3 factories owned by the company. The weights of the products in monthly sales may vary depending on time of the year (demands of certain products shift to others in each of the 4 seasons), age of the products and market conditions, but yearly aggregate demand has a very strong correlation with the price of the product (Here, we ignore any other factor and assume that the yearly aggregate demand is directly and linearly effected by the price). The company found out that when the price for a packet of 20 herbal tea bags is 10 TL, yearly demand is 337500 packets. When the price increases to 11 TL, demand decreases to 337125 packets. On the cost side, the company has 1200000 TL of yearly administrative costs regardless of the price or the number of units sold, including the rents, depreciation of the buildings and other related assets and salaries of 58 workers (average monthly salary…Metropolitan Hospital has estimated its average monthly bed needs as N=1,000+9X where X=timeperiod(months);January2002=0 N=monthlybedneeds Assume that no new hospital additions are expected in the area in the foreseeable future. The following monthly seasonal adjustment factors have been estimated, using data from the past five years: Forecast Metropolitans bed demand for January, April, July, November, and December 2007. If the following actual and forecast values for June bed demands have been recorded, what seasonal adjustment factor would you recommend be used in making future June forecasts?
- The Questor Corporation has experienced the following sales pattern over a 10-year period: Compute the equation of a trend line (similar to Equation 5.4) for these sales data to forecast sales for the next year. (Let 2004=0,2005=1, etc., for the time variable.) What does this equation forecast for sales in the year 2014? Use a first-order exponential smoothing model with a w of 0.9 to forecast sales for the year 2014.Bell Greenhouses has estimated its monthly demand for potting soil to be the following: N=400+4X where N=monthlydemandforbagsofpottingsoil X=timeperiodsinmonths(March2006=0) 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: Forecast Bell Greenhouses demand for potting soil in March, June, August, and December 2007. 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.Tom Glass forecasts electrical demand for the Flatlands Public Power District (FPPD). The FPPD wants to take its Comstock power plant out of service for maintenance when demand is expected to be low. After shutdown, performing maintenance and getting the plant back on line takes two weeks. The utility has enough other generating capacity to satisfy 1,550 megawatts (MW) of demand while Comstock is out of service. Table shows weekly peak demands (in MW) for the past several autumns. When next in year 6 should the Comstock plant be scheduled for maintenance?
- 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 320Q4 (i) 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) =6t2 + 5t (t + 1)2. What happens to production in the long run ? (ii) 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.Assuming the oil slick is continuously distributed,how thick would you expect it to be at the source?Worldwide annual sales of a device in 2012–2013 were approximately q = −6p + 3,040 million units at a selling price of $p per unit. Assume a manufacturing cost of $40 per unit. [HINT: Recall that Profit = Revenue − Cost.] Find the function P for annual profit, in millions of dollars and in terms of p only, subject to any constraints. P(p) = ____ Find P′(p). P′(p) = ____ What selling price (in dollars) would have resulted in the largest annual profit? (Round your answer to two decimal places.) p = $____ What would have been the resulting annual profit (in millions of dollars)? (Round your answer to the nearest whole number.) $ ____ million