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- A company manufacturers a product in the United States and sells it in England. The unit cost of manufacturing is 50. The current exchange rate (dollars per pound) is 1.221. The demand function, which indicates how many units the company can sell in England as a function of price (in pounds) is of the power type, with constant 27556759 and exponent 2.4. a. Develop a model for the companys profit (in dollars) as a function of the price it charges (in pounds). Then use a data table to find the profit-maximizing price to the nearest pound. b. If the exchange rate varies from its current value, does the profit-maximizing price increase or decrease? Does the maximum profit increase or decrease?Although the normal distribution is a reasonable input distribution in many situations, it does have two potential drawbacks: (1) it allows negative values, even though they may be extremely improbable, and (2) it is a symmetric distribution. Many situations are modelled better with a distribution that allows only positive values and is skewed to the right. Two of these that have been used in many real applications are the gamma and lognormal distributions. @RISK enables you to generate observations from each of these distributions. The @RISK function for the gamma distribution is RISKGAMMA, and it takes two arguments, as in =RISKGAMMA(3,10). The first argument, which must be positive, determines the shape. The smaller it is, the more skewed the distribution is to the right; the larger it is, the more symmetric the distribution is. The second argument determines the scale, in the sense that the product of it and the first argument equals the mean of the distribution. (The mean in this example is 30.) Also, the product of the second argument and the square root of the first argument is the standard deviation of the distribution. (In this example, it is 3(10=17.32.) The @RISK function for the lognormal distribution is RISKLOGNORM. It has two arguments, as in =RISKLOGNORM(40,10). These arguments are the mean and standard deviation of the distribution. Rework Example 10.2 for the following demand distributions. Do the simulated outputs have any different qualitative properties with these skewed distributions than with the triangular distribution used in the example? a. Gamma distribution with parameters 2 and 85 b. Gamma distribution with parameters 5 and 35 c. Lognormal distribution with mean 170 and standard deviation 60Graph the feasible region for the system of inequalities. 5x+y< -3 x-y > 3
- The relationship between temperature measured on the Celsius scale and on the Fahrenheit scale is linear. The freezing point of water is 0°C and 32°F, and the boiling point is 100°C and 212°F. (a) Find an equation giving the relationship between the temperature F measured on the Fahrenheit scale and the temperature C measured on the Celsius scale.F = (b) Find F as a function of C, and use this formula to determine the temperature in Fahrenheit corresponding to a temperature of 20°C. (Round your answer to one decimal place.)°F(c) Find C as a function of F, and use this formula to determine the temperature in Celsius corresponding to a temperature of 80°F. (Round your answer to one decimal place.)°CGraph the feasible region for the system of inequalities. 4x+y≤3 x-y>3What would the formula be for Cells B9 and C9 be to populate 0? Or is it just left blank?
- It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico: x 5.00 6.00 6.75 7.00 7.50 y 3 57 75 71 71 What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? Round your answer to the nearest tenth of a percent. a.81.9% b.0.9% c.90.5% d.3.3%In the figure below, no probabilities are known for the occurrence of the nature states. For the matrix, solve every one of the subpoints with the respective formulas: Laplace Maximin(Minimax) Savage Hurwitz (assume that α=0.3)Define the different components (y, x, a, and b) of a linearregression equation
- The following data relate the sales figure of the bar in Mark Kaltenbach's small bed- and -breakfast inn in portland, to the number of guest registered that week: week guests bar sales 1 16 $320 2 12 $265 3 18 $390 4 14 $315 a) the simple linear equation that relates bar sales to the number of guests ( not totime) is (round your response to one decimal place) Bar sales=[__]+[__]X guestFor f(x) = 3 + 7x − 19x^2 + 2x^4, use complete Horner’s algorithm to find (a) the Maclaurin series (Taylor series about x = 0) (b) the Taylor series for this function about x = 2.Long-Life Insurance developed a linear model to determine the amount of term life insurance a family of four should have, based on the head of the household's current age. The equation is: y = 163 -0.45xwherey = Insurance needed ($000)x = Current age of head of household Calculate the amount of term life insurance you would recommend for a family of four if the head of the household is 53 years old. (Round your answer to 2 decimal places.)