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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?Suppose that the number of ounces of soda put into aPepsi can is normally distributed, with m 12.05 oz ands .03 oz.a Legally, a can must contain at least 12 oz of soda.What fraction of cans will contain at least 12 oz of soda?b What fraction of cans will contain under 11.9 oz ofsoda?c What fraction of cans will contain between 12 and12.08 oz of soda?d 1% of all cans will contain more than oz.e 10% of all cans will contain less than oz.f Pepsi controls the mean content in a can by setting atimer. For what mean should the timer be set so that only1 in 1,000 cans will be underfilled?b. The following table shows the number of televisions sold over the last ten years at alocal electronic store. YEAR TV SALES 1 1502 3003 4804 6005 6306 6407 7008 8259 90010 980 i. Using trend projection, develop a formula to predict sales for years 11 and 12. Youhave to show all working. You will need to develop a table to calculate the slope andthe intercept.
- We are considering investing in three stocks. The randomvariable Si represents the value one year from now of $1invested in stock i. We are given that E(S1) 1.15, E(S2) 1.21, E(S3) 1.09; var S1 0.09, var S2 0.04, var S3 0.01; cov(S1, S2) 0.006, cov(S1, S3) 0.004, and cov(S2,S3) 0.005. We have $100 to invest and want to have anexpected return of at least 15% during the next year.Formulate a QPP to find the portfolio of minimum variancethat attains an expected return of at least 15%.b. The following table shows the number of televisions sold over the last ten years at alocal electronic store.YEAR TV SALES1 1502 3003 4804 6005 6306 6407 7008 8259 90010 980i. Using trend projection, develop a formula to predict sales for years 11 and 12. Youhave to show all working. You will need to develop a table to calculate the slope andthe intercept. ii. Use that formula to forecast television sales for years 11 and 12.A golf club manufacturer is trying to determine how the price of a set of clubs affects the demand for clubs. The file P10_50.xlsx contains the price of a set of clubs and the monthly sales. Assume the only factor influencing monthly sales is price. Fit the following three curves to these data: linear (Y = a + bX), exponential (Y = abX), and multiplicative (Y = aXb). Which equation fits the data best? Interpret your best-fitting equation. Using the best-fitting equation, predict sales during a month in which the price is $470. File data: Price Demand $400 20,000 $420 19,000 $440 17,000 $460 16,000 $500 14,000 $380 22,000 $290 31,000 $340 26,000 $220 41,000 $700 6,000
- We must invest all our money in two stocks: x and y.The variance of the annual return on one share of stock x isvar x, and the variance of the annual return on one share ofstock y is var y. Assume that the covariance between theannual return for one share of x and one share of y is cov(x,y). If we invest a% of our money in stock x and b% in stocky, then the variance of our return is given by a2var xb2var y2ab cov(x, y). We want to minimize the variance of thereturn on our invested money. What percentage of the moneyshould be invested in each stock?53. Why is the RISKCORRMAT function necessary?How does @RISK generate random inputs by default,that is, when RISKCORRMAT is not usedA building contains 1000 lightbulbs. Each bulb lastsat most five months. The company maintaining thebuilding is trying to decide whether it is worthwhileto practice a “group replacement” policy. Under agroup replacement policy, all bulbs are replaced everyT months (where T is to be determined). Also, bulbsare replaced when they burn out. Assume that it costs$0.05 to replace each bulb during a group replacementand $0.20 to replace each burned-out bulb if it isreplaced individually. How would you use simulationto determine whether a group replacement policy isworthwhile?
- We all hate to bring small change to the store. Usingrandom numbers, we can eliminate the need for change andgive the store and the customer a fair shake.a Suppose you buy something that costs $.20. How could you use random numbers (built into the cash reg-ister system) to decide whether you should pay $1.00 or nothing? This eliminates the need for change!b If you bought something for $9.60, how would youuse random numbers to eliminate the need for change?c In the long run, why is this method fair to both thestore and the customer?4. A publisher prints copies of a popular weekly tabloid for distribution and sale. The fixed costs are $500 per print run, with each copy printed costing an additional $0.40. If C(q) is the cost function (in $) of the price of the print run as a function of copies printed, what is the formula for C(q)? Select one: a. C(q) = 500 + 0.4q b. C(q) = 500q + 0.4 c. C(q) = (500 + 0.4)q d. C(q) = 500 - 0.4q e. C(q) = 500q - 0.4 5. A hot dog vendor sells an average of 50 hot dogs during a Little League baseball game. If the sales are Normally distributed with a standard deviation of 7 hot dogs, what is the probability the vendor will sell between 45 and 65 hot dogs? Select one: a. 74.50% b. 92.36% c. 99.78% d. 174.50% e. 2.14 f. -0.71 g. 0.71Which of the following statements is correct for the Black-Scholes model? A) The price of an American call written on a stock is: c = SN(d1)-Ke-rTN(d2) B) The stock price at a future point in time follows a log-normal distribution. C) The continuously compounded return on the stock follows a log-normal distribution. D) Black-Scholes prices may allow for arbitrage opportunities. Please explain and justify your choice.