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## 22912 MTH 1007 Operations Research -- Spring 2012 On Line Course Quiz 3

This web page is http://www.bernstein-plus-sons.com/.dowling/MTH1007S12/MTH1007_Quiz_3.html

This is the third quiz for MTH 1007 to be taken on Friday, 17 February 2012 after completing the assignment. It should take you between half an hour and an hour to answer these questions.

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Please answer the following questions on this form (or on a paper copy of this form).

1. A broker offers you a chance to invest \$1000 into a stock on margin. The proability of making \$1,000,000 is 5%. The probability of making \$100,000 is 45%. The probability of making \$50,000 is 10%. The probability of losing \$10,000 is 30%. The probability of losing \$1,000,000 is 20%. What is the total of all the probabilities just given. Say something significant about that total.

2. It costs \$20,000,000 to build a factory to produce up to 250,000 widgets per year. The unit cost of producing one widget is \$5000. You can sell widgets for \$10,000 each. The probability that you will be able to sell only 1000 units is 0.1. The probability that you will be able to sell 5000 units is 0.2. The probability that you will be able to sell 10000 units is 0.6. The probability that you will be able to sell 50000 units is 0.1. What is the mean, standard deviation and mean absolute deviation of the number of units you expect to be able to sell.

3. It costs \$20,000,000 to build a factory to produce up to 250,000 widgets per year. If the unit cost of producing one widget is \$5000. You can sell widgets for \$10,000 each. The probability that you will be able to sell only 1000 units is 0.1. The probability that you will be able to sell 5000 units is 0.2. The probability that you will be able to sell 10000 units is 0.6. The probability that you will be able to sell 50000 units is 0.1. What is the mean, standard deviation and mean absolute deviation of the profit or loss you can expect from this operation.

4. Explain how to build a payoff table both using a specific example and using coherent sentences to explain the process.

5. When events A and B are independent, what is the probability of A and B?

6. You have \$10,000 to invest in the stock market. You are considering only 2 possible stocks, FBN (for Fly by Night) and ASL (for Allied Swamp Land). The probability of FBN increasing by 100% is 10%. The probability of FBN increasing by 10% is 40%. The probability of FBN decreeasing by 10% is 30% and the probability of FBN decreasing by 80% is 20%. The probability of ASL increasing by 1000% is 1%. The probability of ASL increasing by 1% is 49%. The probability of ASL becoming worthless is 50%. Even though FBN and ASL have the same directors and officers and even though they use the same Cayman Islands post-office box as an office, you are to assume the that outcomes for both stocks are independent. You will invest all of the \$10,000 in one the other or both in units of \$2,500. Work out a complete table of payoffs with columns being states of stated probabilities and rows being allocations strategies. The first row would be 100% in FBN. The fifth and last row would be 100% in ASL.

7. What is the minimax strategy? Give a concrete example. Explain how it relates to the maximax, maximin and maximean strategies.

8. What is a regret table. Give a specific example. Explain the minimax regret strategy.

9. Return to question 6. Compute the expected payoff for each of the 5 investment alternatives. Which gives the best expected payoff?

10. Return to question 6. Compute the expected regret for each of the 5 investment alternatives. Which gives the minimum expected regret?

11. What is the risk-constrained expected payoff criterion? Show how to apply it to question 6.

12. What is the payoff-constrained minimum risk criterion? Show how to apply it to question 6.

13. Using α=3, apply the SD-based payoff at risk criterion to question 6.

14. Explain replacement analysis.

<==== Do this AFTER you've answered all the questions

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Revised 12 February 2012