Virtual Classroom

ARE 335

MATHEMATICAL PROGRAMMING FOR ECONOMISTS

Fall 1996, Instructor: Dr. Tsoung-Chao Lee

INVERSE.ZIP - click to download a simple program for solvimg a system of simultaneous equations Ax = b. Output includes inverse A, the solution for x = inv(A)*b, and det(A).

FERTCOST.ZIP - click to download a simple program for finding the least fertilizer cost with a certain N-P-K combination.

LPTEST.ZIP - click to download a set of files for testing your basic knowledge in linear programming. Unzip the file and type LPTEST to start the self test. Part I is true/false choice and Part II is multiple choice.

LPQP - Version 3.1 solves linear, quadratic, and integer programming problems with simplex methods. It accepts alternative inputs, sends results to a file or printer. It shows simplex tableau on screen. It identifies infeasible, feasible, unbounded, inconsistent, optimal, multiple, and integer solutions. The tableau can be revised easily. It is menu driven. It is programmed by the instructor for learning purpose. It will show intermediate simplex tableaux if you request. Students registered ARE 335 may bring your own disk to obtain a copy. It is copy protected! The program is currently set at 100 variables and 80 constraints. Students in the class need it to solve exercises and the term project. During the first 3 weeks, students learn calculations by hand. The software will not be available until after 9/19/96.

Exercise #7 - Do not forget to specify the constraint on the output unit. Otherwise, your least cost will be erroneously 0. You must use LPQP in this exercise.

LPQP.DAT - an example LP input file in LPQP (for exercise #7).

LP.GMS - an example LP file in GAMS (for exercise #8).

NPK.MVS - an example LP file in MPSX/370 (for exercise #10).

TEMPLATE.BAS - a template of BASIC program for solving binary and integer programming problem. The program can be used to check the solutions for exercises #16 and #17 that are solved by GAMS.

Exercises #16-19 - When working with GAMS, make sure =l= is typed as =L= so that L is not mistaken to be one in between the equality signs. The same thing applies to specifying the level of variables, such as X.L instead of X.l because the latter looks like X.1. Also that when you are using MIP, GAMS always warns you that the solution may not be optimal. Add another constraint to demand that the objective function be larger than the existing optimum, and run it again until no more feasible solution can be obtained.

HOUSE.TXT - Problem formulations for Exercise #17.

GAMS - Introduction to the GAMS system. You can download the example problems and GAMS programs.

Grades for ARE 335, Mathematical Programming for Economists, Fall 1996

For the final exam:
Mean = 81.47,  variance =307.78,  Std Dev = 17.54
 
For the course:
Grade course  Midterm  Paper Excercise Final formula1 formula2 Student
  A    95.50   91.50   98.00   98.00   96.00   95.50   94.60    4358
  A    95.33   87.30   95.00   95.70   98.00   95.33   93.19    1814
  A    93.93   96.50   84.00   93.30   94.00   93.43   93.93    1836
  A    90.60   93.00   84.00   92.00   89.50   89.90   90.60    2449
  A-   88.81   84.00   95.00   94.10   88.50   88.81   87.91    2177
  B+   85.72   76.00   80.00   85.20   90.00   85.72   82.92    1823
  B    81.52   77.50   85.00   92.20   80.50   81.52   80.92    3301
  B    80.53   73.30   80.00   86.70   82.00   80.53   78.79    4924
  B    80.15   82.50   85.00   88.50   74.50   78.55   80.15    6496
  B    79.37   85.80   85.00   71.50   73.50   76.91   79.37    7740
  B    79.33   70.00   85.00   91.30   79.50   79.33   77.43    8417
  F    26.86   66.50    0.00    2.60    0.00   13.56   26.86    2583

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