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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 8

This web page is http://www.bernstein-plus-sons.com/.dowling/MTH1007F13/MTH1007_Quiz_8.html

This is the eighth quiz for MTH1007 to be taken on Tuesday, 12 November 2013. This quiz should be taken after reading Chapter 4 and making a second 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 these problems and to show your work in detail.

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Please fill in the following information:

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

1. You are going to produce stuffed animals: a cuddly dog, a cute cat, a giant panda and a tiny little alligator. The animals require supplies of plastic, cloth and stuffing. The following table shows the amount of each supply used for each animal, the total available weight of each supply, and the cost per pound of each supply. The last column shows the retail price you can get for each animal.

 plastic cloth stuffing retail price dog 0.1 lbs 0.2 lbs 2 lbs \$12 cat 0.1 lbs 0.1 lbs 1 lb \$8 panda 0.2 lbs 0.5 lbs 5 lbs \$35 alligator 0.05 lbs 0.03 lbs .2 lbs \$3 total available 100 lbs 300 lbs 1000 lbs cost per pound \$0.10 \$2.00 \$0.25

The dog and the cat have to be made on the same machine so, in the time you have available, you will only be able to make a total of 500 dogs plus cats (e.g. 200 dogs and 300 cats). In the time you have available, you can make only 100 pandas and no more than 2000 alligators. Your retailers have room for all the alligators you can make but every panda takes the space of 4 dogs or 6 cats and if it were all pandas, there would only be space for 50 pandas.

Rewrite this problem as a linear programming problem, i.e. as a set of linear equaltions giving the payoff (or profit) to be maximized as a variable P that depends linearly on the variables dog, cat, panda and alligator with linear constraints as inequalities. You should have seven inequalities. WHen you write your inequalities, use >= and <= instead of ≥ and ≤.

2. Take the linear programming problem from question 1, put it in standard form and convert each linear inequaity to an equation by introducing slack variables. Show your work.

3. Take the work you have done in questions 1 and 2, write the tableau to apply the simplex method to the linear programming problem and do the first 2 pivots. Show your work and show all three resulting tableaux.

4. Complete the linear programming problem in the prior question, finding the optimal numbers of each type of stuffed animal to make. Show the final tableau.

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Revised 20 October 2013