Linear programing problem

Elmountassir billah e.

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Linear programing problem

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Linear programing, exercice, operations, canonical form, mathematical formalization, direction vector, economic interpretation, total margin, free margin, succession, graph, Method Potential Metra, calendar

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Abstract

For a given problem, the following questions are answered:
Give the mathematical formalization, in canonical form, of this linear program (primal program);
1. Graphically determine the optimal production of chairs and tables;
2. What is the economic interpretation of these results?
3. Is the optimal production degenerate (give the definition of the degeneration of the 1st and 2nd
type)?
4. Write the primal program in standard form;
5. The transition from the canonical form to the standard form is done by adding the deviation variables. What is the economic interpretation of each of them?
6. Find the optimal production via the simplex algorithm (write the numbers inside the three simplex tables as fractions);
7. If we produce 10 tables, how much would it be necessary to reduce this production to produce 4 chairs?
8. Write the dual of the primal program;
9. Give the final table of the dual program from that of the primal program.

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[...] This is not the case in our example. 2nd type: An optimal solution is said to be degenerate if more than two constraints compete at this point. This is not the case in our example.     The passage from the canonical form of the program primal à the shape standard herself fact by adding of three gap variables e1, e and e3: The economic interpretation of each of the variance variables: e1 : available working hours per week and not used e2 : the amount of wood available per week and not used e3 : the amount of fabric available per week and not used Let's find the optimal production via the simplex algorithm: The solution of base admissible east x e e e3 )  . [...]

[...] Is the optimal production degenerate (give the definition of the degeneration of the 1st and 2nd type)? Write the primal program in standard form; The transition from the canonical form to the standard form is done by adding the deviation variables. What is the economic interpretation of each of them? Find the optimal production via the simplex algorithm (write the numbers inside the three simplex tables as fractions); If we produce 10 tables, how much would it be necessary to reduce this production to produce 4 chairs? [...]

[...] G and is equal to 7 (resp and that is, the maximum delay that can be made to start the execution of this task is 7 days (resp and without changing the start date at the latest of task D (resp. I and the free margin of task B (resp. D and is equal to 2 (resp and that is, the maximum delay that can be made at the start of the execution of this task is 2 days (resp and without changing the start date at the earliest of task D (resp. [...]

[...] G and Any delay in starting the execution of tasks F and G changes the start date of tasks G and I at the earliest. Indeed, the free margins of these tasks are zero. [...]

[...] Optimal production A is the solution of the following system: x x x2  16 x x x 15 10 - x1 - 5 z max  2400 - 10 ( x1  4x2  40 x1  x1  10 vertical straight The economic interpretation of the results: The company uses all available working hours (the first constraint is saturated x1  4x2  40 and all the available wood (the second constraint is saturated x1  x2  16 ) ) but it has 2 left unused tissue units (the third stress is unsaturated x1  8  10 ) to produce 8 chairs and 8 tables per week ( A  8,8) and thus achieve a maximum turnover of 2400 UM ( zmax  (100   (200   2400 Definition of degeneration: there are two types of degeneration: 1st type: This is the case where the direction coefficient of the line representing the economic function is identical to that of the line representing a non-redundant constraint. So, there are an infinite number of solutions. [...]

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