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## 20382 MTH 1007 Operations Research -- Spring 2012 On Line Course Quiz 2

This web page is http://www.bernstein-plus-sons.com/.dowling/MTH1007S12/MTH1007_Quiz_2.html

This is the second quiz for MTH 1007 to be taken on Friday, 10 February 2012 after completing the first 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. 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. What is the break-even point in producing widgets?

2. 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. You expect sales to be normally distributed with a mean of 20,000 units and a standard deviation of 10,000 unit. Looking at profit, what is the 5% value at risk?

3. Give the Z-score for the 5th and 95th oercentiles.

4. If sales are normally distributed with a mean of 250,000 and a standard deviation of 50,000, what are the sales ranges for the 5th, 20th, 80th and 95th percentiles?

5. Give a recent example of gambler's ruin.

6. If the probability of losing \$1,000,000 is 10%, the probability of just breaking even is 40%, the probability of making \$500,000 is 20% and the probability of making \$2,000,000 is 30%, what is the expected profit?

7. Compute the standard deviation of the prior example.

8. Give the Z-score and perentile for a loss in the prior example.

9. What is the Mean Absolute Deviation?

10. Compute the Mean Absolute Deviation for the example in question 6 and compare it to the standard deviation.

11. A broker offers you a chance to invest \$1000 into a stock on margin. If all goes well, you will make \$100,000. If things go badly, you could owe as much as \$200,000. The probability of things going well is 80%. The probability of things going badly is 20%. Carefully explain the considerations in making a decision on this investment.

12. 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 expected return on this investment?

13. 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 probability of taking a loss on this investment?

14. Give the procedure for calculating β.

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

You probably DON'T want to do this ===>

Revised 8 January 2012