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rec10_1

# rec10_1 - ± 1 ± 2 as well as larger ones like ± 1 ± 2(c...

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ORIE 3300/5300 RECITATION 10 Fall 2010 Week of November 15. Do this exercise with your declared partner (if you have one). In this session you will test the economic interpretation of the dual vari- ables. Consider the linear program maximize c T x subject to Ax = b x 0 , where A = 2 1 3 1 0 0 2 3 1 0 1 0 1 1 2 0 0 1 , b = 7 6 4 , c = 5 3 9 0 0 1 (a) Solve this linear program using AMPL. For this, you should write a model file for a standard equality form problem using A , b , and c as parameters, and a corresponding data file. (b) By experimenting with small changes to the vector b , estimate the rate of change of the optimal value with respect to each of b 1 , b 2 , and b 3 . Try small changes like ± . 1 , ± . 2 as well as larger ones like
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Unformatted text preview: ± . 1 , ± . 2 as well as larger ones like ± 1 , ± 2. (c) Solve the dual linear program using AMPL, and compare your answer with the rates of change in part (b). Again, you need to write a model ﬁle that represents the dual of the problem you modelled in (a); the data ﬁle can be the same. (d) Use AMPL to calculate the “marginal values” associated with the con-straints of the primal problem. (See page 17 of the AMPL book.) Compare your answers with part (c). (e) (Not to be turned in.) Think about why the linear behavior of the ob-jective function for small changes no longer holds when larger changes are made. 1...
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