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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 9

This web page is http://www.bernstein-plus-sons.com/.dowling/MTH1007F13/MTH1007_Quiz_9.html

This is the nineth quiz for MTH1007 to be taken on Tuesday, 19 November 2013. This quiz should be taken after reading Chapter 4 and making a final pass at viewing the videos on linear programming and the simplex method. It should take you between half an hour and two hours to answer these questions, if you are well prepared, more time if not. It is very important to do both these problems and to show your work in detail.

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

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Please fill in the following information:

Name:

Email:

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

1. You have a total budget of \$120,000,000 for factory construction. You make widgets. It costs \$20,000,000 to make a medium-sized widget factory that can make up to 10,000 widgets per year at a unit cost of \$6000 per widget. It costs \$50,000,000 to make a large-sized widget factory that can make up to 50,000 widgets at a unit cost of \$5000 per widget. You can sell widgets for \$10,000 each. The demand for widgets is normally distributed with a mean of 75,000 widgets per years and a standard deviation of 30,000 widgets per year. Explain what issues you would consider and how you would make the decision on what plants to build of what size.

2. You have a factory that can make cars and SUVs. Each car you build needs 1000 pounds of metal at \$7.50 per pound and 2000 pounds of plastics at \$3.00 per pound. Each SUV you build needs 2,500 pounds of metal at \$7.50 per pound and 4,000 pounds of plastic at \$3.00 per pound. You can sell a car for \$25,000 and an SUV for \$50,000. You can make a total of no more than 1,000,000 cars or SUVs (e.g. 250,000 cars and 750,000 SUVs or 500,000 cars and 500,000 SUVs, etc., per year. You can get no more than 1,500,000,000 pounds of metal and no more than 3,000,000,000 pounds of plastic per year. Your cars get 30 miles per gallon and you SUV's get 15 miles per gallon. Federal law requires you to get a fleet average of at least 20 miles per gallon. Prepare an analysis of this problem, first in words and then as a simplex tableau, that you take steop-by-step to a solution.

3. Explain what is similar and what is different about the first 2 questions on this quiz and how you solve them.

4. Explain the concept of a binding constraint and of a shadow price, both in words and by giving a completely worked numeric example.

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

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

Revised 20 October 2013