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# Methods of Optimization - version 30

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**31.07.2013**

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# Description

Task 1 - 100

Below are expanded matrix for 100 variants of systems of linear equations. In all embodiments.

It is necessary, using the method of complete elimination of unknowns (Gauss-Jordan), to find any common solutions and the three basic systems. Make checks. The solution recommended to submit a tablitsy.Zadachi 201 - 300

Each version contains tables in which the conditions written canonical linear programming problem to a minimum, ie. E. In the first line put the coefficients of the objective function. The other lines in the first five columns vectors are conditions, and recorded in the last column vector constraints. In the upper right corner of the table contains the purpose of the task.

It is necessary to carry out the following tasks.

1. Problem solved graphically

2. Using the simplex method to solve the problem or to determine that the problem has no solution.

3. Construct the dual problem. If the vector is found, calculate the optimal plan for the dual problem using the first duality theorem. Calculate the value of the function

4. To analyze the obtained solution using the complementary slackness condition

If, then. If, then.

Tasks 401 - 500

Below are the complete linear programming problem. It should be done in the order specified the following tasks.

1. Find an optimal plan for the direct problem graphically.

2. Construct the dual problem.

3. Find the optimal program of the dual problem of the line graphics solutions using the complementary slackness condition.

4. Find the optimal plan for the direct problem of the simplex method (for the construction of the initial support program is recommended to use an artificial basis).

5. Find an optimal plan for the dual problem of the first duality theorem using the final simplex tableau obtained by solving the direct problem (see. P. 4). Check the statement "the objective function value pair of dual problems of optimal solutions for their match."

6. The dual problem to solve by the simplex method, then use the final simplex table of the dual problem to find the best plan for the direct problem for the first duality theorem. Compare the result with the result obtained by the graphical method (see. P.1).

Tasks 501-600

The following are the numeric data transport problems. Transportation cost per unit of output recorded in the cells of the table. Stocks listed on the right of the tables and needs - from below. Required to construct the initial plan means "north-west corner," "minimum elements" by Vogel. Because each plan to find the best plan for the method of potentials.

Tasks 601 - 700

Below 100 variants of the transportation problem in the network statement. Each task is displayed in the form of an undirected connected graph. On the edges of the recorded values \u200b\u200bof specific values \u200b\u200bon top (in circles) - value of stocks needs. Build a valid test plan, test it for optimality. If necessary, bring to the optimal plan by potential

Tasks 701 - 800

Below are the tables in the cells surrounding the elements of the efficiencies of the problem of picky bride. It is necessary to find the best choice, in which the average length of family life of each family will be greatest. Solve the problem by building and Hungarian method.