J&J has given you $12 million to spend on advertising Huggys diapers during the next 12 months. Atthe beginning of January, Huggys has a 30% market7.9 Conclusion 401share. During any month, 10% of the people whopurchase Huggys defect to brand X, and a fraction0.2a1y2 of customers who usually buy brand X switchto Huggys, where a is the amount spent on advertisingin millions of dollars. For example, if you spend $4million during a month, 40% of brand X’s customersswitch to Huggys. Your goal is to maximize J&J’saverage market share during the next 12 months,where the average is computed from each month’sending share. Determine an appropriate advertisingpolicy. (Hint: Make sure you enter a nonzero trialvalue for each month’s advertising expense or Solvermight give you an error message.)

J&J has given you $12 million to spend on advertising Huggys diapers during the next 12 months. Atthe beginning of January, Huggys has a 30% market7.9 Conclusion 401share. During any month, 10% of the people whopurchase Huggys defect to brand X, and a fraction0.2a1y2 of customers who usually buy brand X switchto Huggys, where a is the amount spent on advertisingin millions of dollars. For example, if you spend $4million during a month, 40% of brand X’s customersswitch to Huggys. Your goal is to maximize J&J’saverage market share during the next 12 months,where the average is computed from each month’sending share. Determine an appropriate advertisingpolicy. (Hint: Make sure you enter a nonzero trialvalue for each month’s advertising expense or Solvermight give you an error message.)

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 59P

See similar textbooks

Similar questions

In Example 11.1, the possible profits vary from negative to positive for each of the 10 possible bids examined. a. For each of these, use @RISKs RISKTARGET function to find the probability that Millers profit is positive. Do you believe these results should have any bearing on Millers choice of bid? b. Use @RISKs RISKPERCENTILE function to find the 10th percentile for each of these bids. Can you explain why the percentiles have the values you obtain?
You want to take out a 450,000 loan on a 20-year mortgage with end-of-month payments. The annual rate of interest is 3%. Twenty years from now, you will need to make a 50,000 ending balloon payment. Because you expect your income to increase, you want to structure the loan so at the beginning of each year, your monthly payments increase by 2%. a. Determine the amount of each years monthly payment. You should use a lookup table to look up each years monthly payment and to look up the year based on the month (e.g., month 13 is year 2, etc.). b. Suppose payment each month is to be the same, and there is no balloon payment. Show that the monthly payment you can calculate from your spreadsheet matches the value given by the Excel PMT function PMT(0.03/12,240, 450000,0,0).
Suppose you currently have a portfolio of three stocks, A, B, and C. You own 500 shares of A, 300 of B, and 1000 of C. The current share prices are 42.76, 81.33, and, 58.22, respectively. You plan to hold this portfolio for at least a year. During the coming year, economists have predicted that the national economy will be awful, stable, or great with probabilities 0.2, 0.5, and 0.3. Given the state of the economy, the returns (one-year percentage changes) of the three stocks are independent and normally distributed. However, the means and standard deviations of these returns depend on the state of the economy, as indicated in the file P11_23.xlsx. a. Use @RISK to simulate the value of the portfolio and the portfolio return in the next year. How likely is it that you will have a negative return? How likely is it that you will have a return of at least 25%? b. Suppose you had a crystal ball where you could predict the state of the economy with certainty. The stock returns would still be uncertain, but you would know whether your means and standard deviations come from row 6, 7, or 8 of the P11_23.xlsx file. If you learn, with certainty, that the economy is going to be great in the next year, run the appropriate simulation to answer the same questions as in part a. Repeat this if you learn that the economy is going to be awful. How do these results compare with those in part a?
2) A buyer for a large sporting goods store chain must place orders for professional footballs with the footballmanufacturer six months prior to the time the footballs will be sold in the stores. The buyer must decidein November how many footballs to order for sale during the upcoming late summer and fall months.Assume that each football costs the chain $45. Furthermore, assume that each can be sold for a retail priceof $90. If the footballs are still on the shelves after next Christmas, they can be discounted and sold for$35 each. The probability distribution of consumer demand for these footballs (in hundreds) during theupcoming season has been assessed by the market research specialists and is presented below. Finally,assume that the sporting goods store chain must purchase the footballs in lots of 100 units. Demand Probability 4 0.30 5 0.50 6 0.20 a) Construct a decision tree…
The secondary market is the market wherein:\\nQuestion 2 options:\\n\\nthe government is either the buyer or the seller of the security.\\n\\ninvestors buy from and sell to other investors.\\n\\nthe security issuer is the buyer and the seller is a member of the general public.\\n\\none issuer exchanges securities directly with another issuer.\\n\\nthe security issuer is the seller and the buyer is a member of the general public.
Dataware is trying to determine whether to give a $10 rebate, cut the price $6, or have no price change on a software product. Currently, 40,000 units of the product are sold each week for $45 apiece. The variable cost of the product is $5. The most likely case appears to be that a $10 rebate will increase sales 30%, and half of all people will claim the rebate. For the price cut, the most likely case is that sales will increase 20%.a. Given all other assumptions, what increase in sales from the rebate would make the rebate and price cut equally desirable?b. Dataware does not really know the increase in sales that will result from a rebate or price cut. However, the company is sure that the rebate will increase sales by between 15% and 40% and that the price cut will increase sales by between 10% and 30%. Perform a sensitivity analysis (two-way data table) that could be used to help determine Dataware’s best decision.
We are going to invest $1,000 for a period of 6 months.Two potential investments are available: T-bills and gold. Ifthe $1,000 is invested in T-bills, we are certain to end the6-month period with $1,296. If we invest in gold, there is a34chance that we will end the 6-month period with $400 anda 14chance that we will end the 6-month period with $10,000.If we end up with x dollars, our utility function is given byu(x) x1/2. Should we invest in gold or T-bills?
Spein Company is a diversified company that discloses supplemental financial information on itssegments. The following information is available for 2019:Sales Traceable Costs Allocable CostsSegment X $400,000 $225,000Segment Y 300,000 240,000Segment Z 200,000 135,000Totals $900,000 $600,000 $150,0006Allocable costs are assigned based on the ratio of a segment’s income before allocable costs to totalincome before allocable costs. This is an appropriate method of allocation. Segment Y’s profit for 2019is ____________________.A. 32,400 Small; 8,100 Medium; 1,620 LargeB. 34,808 Small; 8,700 Medium; 1,740 LargeC. 37,010 Small; 9,250 Medium; 1,850 LargeD. 38,505 Small; 9,625 Medium; 1,925 Large
1. Suppose you are going on a weekend trip to a city that is d miles away. Develop a model that determines your round-trip gasoline costs. What assumptions or approximations are necessary to treat this model as a deterministic model? Are these assumptions or approximations acceptable to you? 2. Suppose that a manager has a choice between the following two mathematical models of a given situation: (a)a relatively simple model that is a reasonable approximation of the real situation, and (b)a thorough and complex model that is the most accurate mathematical representation of the real situation possible. Why might the model described in part (a) be preferred by the manager?
Suppose an investor has the opportunity to buy the followingcontract, a stock call option, on March 1. Thecontract allows him to buy 100 shares of ABC stock atthe end of March, April, or May at a guaranteed priceof $50 per share. He can exercise this option at mostonce. For example, if he purchases the stock at the endof March, he can’t purchase more in April or May atthe guaranteed price. The current price of the stock is$50. Each month, assume that the stock price eithergoes up by a dollar (with probability 0.55) or goesdown by a dollar (with probability 0.45). If the investorbuys the contract, he is hoping that the stock price willgo up. The reasoning is that if he buys the contract, theprice goes up to $51, and he buys the stock (that is, heexercises his option) for $50, he can then sell the stockfor $51 and make a profit of $1 per share. On the otherhand, if the stock price goes down, he doesn’t haveto exercise his option; he can just throw the contractaway.a. Use a decision tree…
I need help with everything, please. Formulate the problem and submit formulation - no need to solve. 1. An investment advisor at Shore Financial Services wants to develop a model that can be used to allocate investment funds among four alternatives: stocks, bonds, mutual funds, and cash. For the coming investment period, the company developed estimates of the annual rate of return and the associated risk for each alternative. Risk is measured using an index between 0 and 1, with higher risk values denoting more volatility and thus more uncertainty. Because cash is held in a money market fund, the annual return is lower, but it carries essentially no risk. The objective is to determine the portion of funds allocated to each investment alternative in order to maximize the total annual return for the portfolio subject to the risk level the client is willing to tolerate. Total risk is the sum of the risk for all investment alternatives. For instance, if 40% of a client’s funds are…
Based on Brams and Taylor (2000). Suppose that EliLilly and Pfizer are going to merge. Merger negotiations must settle the following issues: ■ What will the name of the merged corporation be?■ Will corporate headquarters be in Indianapolis(Lilly wants this) or New York (Pfizer wants this)?■ Which company’s chairperson will be chairperson of the merged corporation?■ Which company gets to choose the CEO?■ On the issue of layoffs, what percentage of each company’s view will prevail?Brams developed a remarkably simple method for the two adversaries to settle their differences. (This same method could be used to settle differences between other adversaries, such as a husband and wife in a divorce, Arab and Israel in Middle East, and so on.) Each adversary allocates 100 points between all of the issues. These allocations are listed in the file P04_84.xlsx. For example, Lilly believes headquarters is worth 30 points, whereas Pfizer thinks headquarters is worth only 15 points. Layoffs may be…