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Herbert J. Bernstein Professor of Mathematics and Computer Science
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## 90103 MTH 1007 Operations Research -- Fall 2013 On Line Course Quiz 10

This web page is http://www.bernstein-plus-sons.com/.dowling/MTH1007F13/MTH1007_Quiz_10.html

This is the tenth quiz for MTH1007 to be taken on Tuesday, 26 November 2013. This is a partial review for the final. You are responsible for much more than is covered in this quiz.

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

1. Given the samples 4.75, 4.5, 5.0, 5.25, 5.5, compute the mean, the range, the (estimated) standard deviation and the maximum absolute deviation.

2. Suppose you have a widget factory with fixed costs of \$100,000. Suppose the unit production cost for each widget is \$200. Suppose you can sell each widget for \$1000. How many widgets do you need to sell to break even.

3. It costs \$25,000,000 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 25,000 units and a standard deviation of 5,000 units. Looking at profit, what is the 5% value at risk?

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

5. State Bayes' Theorem and explain each term you use.

6. 10% of the population has X disease. A screening test accurately detects the disease for 60% of the people who actually do have it. The test also incorrectly indicates the disease for 20% of the people who actually don't have it. Suppose a randomly selected person screened for the disease tests postive. What is the probability that they have the disease?

7. Explain the Monty Hall problem in the case of 5 doors, computing specific probabilities.

8. Consider the linear constraints: x ≥ 0, y ≥ 0; 4x + 2y ≤ 8; 2x + 4y ≤ 8. Describe the feasible region, giving very precise coordinates for each corner. Maximize the objective function P = 0.8x + 1.6y subject to these constraints using knowledge of the locations of those corners. Show your work.

9. Consider the linear constraints: x ≥ 0, y ≥ 0; 4x + 2y ≤ 8; 2x + 4y ≤ 8. Maximize the objective function P = 0.8x + 1.6y subject to these constraints by introducing slack variables, creating a tableau and applying the simplex method. Show your work.

10. Carefully explain how to use a data table to run a simulation.

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Revised 20 October 2013