2. Consider a bidding problem similar to that presented in class. You can still either bidhigh or low on either the dam or highway project, or you can not prepare a bid.However, the probabilities and outcomes are given in Tables 2.1 and 2.2.Table 2.1 Probabilities and profits of bid resultsProjectProbability ConditionalProfit [$]BidType ofResultUponBidof Bidof ResultHighWin0.20Table 2.2Lose0.80-50,000DamLowWin0.40Table 2.2Lose0.60-50,000HighWin0.10Table 2.2Lose0.90-100,000HighwayLowWin0.20Table 2.2Lose0.80-100,000Table 2.2 Outcome and probabilities, conditional on winning the bidProbabilityPossibleof OutcomeProjectBidProfit [$],if Bid isType ofBidUponOutcomeWonHigh600,0000.60High-100,0000.40DamLow300,0000.70Low-200,0000.301,200,0000.60HighHigh-200,0000.40HighwayLow600,0000.70Low-300,0000.30a(i) Consider that you want to maximize the Expected Value (EV) of profit. Drawthe decision tree and "work the problem" on the decision tree (i.e., indicate thevarious EV values in "boxes" at the appropriate places).

Answered: 2. Consider a bidding problem similar…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section11.2: Operations Models

Problem 2P: In Example 11.1, the possible profits vary from negative to positive for each of the 10 possible...

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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?
A European put option allows an investor to sell a share of stock at the exercise price on the exercise data. For example, if the exercise price is 48, and the stock price is 45 on the exercise date, the investor can sell the stock for 48 and then immediately buy it back (that is, cover his position) for 45, making 3 profit. But if the stock price on the exercise date is greater than the exercise price, the option is worthless at that date. So for a put, the investor is hoping that the price of the stock decreases. Using the same parameters as in Example 11.7, find a fair price for a European put option. (Note: As discussed in the text, an actual put option is usually for 100 shares.)
If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
Based on Grossman and Hart (1983). A salesperson for Fuller Brush has three options: (1) quit, (2) put forth a low level of effort, or (3) put forth a high level of effort. Suppose for simplicity that each salesperson will sell 0, 5000, or 50,000 worth of brushes. The probability of each sales amount depends on the effort level as described in the file P07_71.xlsx. If a salesperson is paid w dollars, he or she regards this as a benefit of w1/2 units. In addition, low effort costs the salesperson 0 benefit units, whereas high effort costs 50 benefit units. If a salesperson were to quit Fuller and work elsewhere, he or she could earn a benefit of 20 units. Fuller wants all salespeople to put forth a high level of effort. The question is how to minimize the cost of encouraging them to do so. The company cannot observe the level of effort put forth by a salesperson, but it can observe the size of his or her sales. Thus, the wage paid to the salesperson is completely determined by the size of the sale. This means that Fuller must determine w0, the wage paid for sales of 0; w5000, the wage paid for sales of 5000; and w50,000, the wage paid for sales of 50,000. These wages must be set so that the salespeople value the expected benefit from high effort more than quitting and more than low effort. Determine how to minimize the expected cost of ensuring that all salespeople put forth high effort. (This problem is an example of agency theory.)
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?
An investor is considering investing in stocks, real estate, or bonds economic conditions. Suppose that the probabilities for good, stable and poor conditions are 0.2, 0.4 and … (figure it out), respectively. Table 1 shows the payoff returns for the investor’s decision situation. Table 1: Investment returns Economic Conditions Investment Good Stable Poor Stocks R5 000 R7 000 R3 000 Real estate -R2 000 R10 000 R6 000 Bonds R4 000 R4 000 R4 000 Assuming the probabilities of the occurrence of the state of nature are unknown, what will be the best investment alternative; a) If the decision maker is pessimistic about the future state, (3) b) If the decision maker strikes a compromise between the maximin and maximax, assuming the coefficient of pessimism is 0.2. (4) c) If the decision is based on opportunistic loss. (6) d) If we use the equally likelihood criterion
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?
Bilbo Baggins wants to save money to meet threeobjectives. First, he would like to be able to retire 30 years from now with a retirementincome of $23,000 per month for 20 years, with the first payment received 30 yearsand 1 month from now. Second, he would like to purchase a cabin in Rivendell in10 years at an estimated cost of $320,000. Third, after he passes on at the end of the20 years of withdrawals, he would like to leave an inheritance of $1,000,000 to hisnephew Frodo. He can afford to save $2,100 per month for the next 10 years. If hecan earn an 11 percent EAR before he retires and an 8 percent EAR after he retires,how much will he have to save each month in Years 11 through 30?
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.)
Suppose you are going to receive $20,000 per year forfive years. The appropriate interest rate is 7 percent.a. What is the present value of the payments if they are in the form of an ordinaryannuity? What is the present value if the payments are an annuity due?b. Suppose you plan to invest the payments for five years. What is the future valueif the payments are an ordinary annuity? What if the payments are an annuitydue?c. Which has the highest present value, the ordinary annuity or annuity due? Whichhas the highest future value? Will this always be true?
2. Provident Capital Corp. specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client contacted Provident with P2,000,000 available to invest. Provident’s investment advisor recommends a portfolio consisting of two investment funds: the Dynamic fund and the Diversified fund. The Dynamic fund has a projected annual return of 10%, and the Diversified fund has a projected annual return of 8%. The investment advisor requires that at most P1,400,000 of the client’s funds should be invested in the Dynamic fund. Provident’s services include a risk rating for each investment alternative. The Dynamic fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per P40,000 invested. The Diversified fund has a risk rating of 4 per P40,000 invested. For example, if P400,000 is invested in each of the two investment funds, Provident’s risk rating for the portfolio would be 6(10) + 4(10) = 100. Finally, Provident developed…
In the time interval between t and t 1 seconds beforethe departure of Braneast Airlines Flight 313, there is aprobability pt that the airline will receive a reservation for 19.4 Further Examples of Probabilistic Dynamic Programming Formulations 1035 the flight and a probability 1 pt that the airline will receiveno reservation. The flight can seat up to 100 passengers. Atdeparture time, if r reservations have been accepted by theairline, there is a probability q(y|r) that y passengers willshow up for the flight. Each passenger who boards the flightadds $500 to Braneast’s revenues, but each passenger whoshows up for the flight and cannot be seated receives $200in compensation. Formulate a dynamic programmingrecursion to enable the airline to maximize its expectedrevenue from Flight 313. Assume that no reservations arereceived more than 100,000 seconds before flight time.

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