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    Lección Simplex

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    Johnn Jimenez
    The document lists 19 optimization problems to solve using the Simplex method. The problems involve maximizing linear objective functions subject to various inequality constraints, and require finding the optimal solution values for variables constrained to be non-negative. The Simplex method is to be applied to solve each problem and determine the maximum value that can be achieved for the given objective function within the feasible region defined by the constraints.

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    Lección Simplex

    Uploaded by

    Johnn Jimenez
    11 views3 pages
    The document lists 19 optimization problems to solve using the Simplex method. The problems involve maximizing linear objective functions subject to various inequality constraints, and require finding the optimal solution values for variables constrained to be non-negative. The Simplex method is to be applied to solve each problem and determine the maximum value that can be achieved for the given objective function within the feasible region defined by the constraints.

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    The document lists 19 optimization problems to solve using the Simplex method. The problems involve maximizing linear objective functions subject to various inequality constraints, and require finding the optimal solution values for variables constrained to be non-negative. The Simplex method is to be applied to solve each problem and determine the maximum value that can be achieved for the given objective function within the feasible region defined by the constraints.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    11 views3 pages

    Lección Simplex

    Uploaded by

    Johnn Jimenez
    The document lists 19 optimization problems to solve using the Simplex method. The problems involve maximizing linear objective functions subject to various inequality constraints, and require finding the optimal solution values for variables constrained to be non-negative. The Simplex method is to be applied to solve each problem and determine the maximum value that can be achieved for the given objective function within the feasible region defined by the constraints.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 3

    INVESTIGACIÓN DE OPERACIONES (6SA)

    UNIVERSIDAD AGRARIA DEL ECUADOR


    INGENIERÍA EN COMPUTACIÓN E INFORMÁTICA

    16-6-2016

    MÉTODO SIMPLEX
    Resolver los siguientes ejercicios con el método Simplex:
    1. Maximizar Z = 2x1 – 4x2 + 5x3 – 6x4
    Sujeta a:
    x1 + 4x2 – 2x3 + 8x4 ≤ 2
    -x1 + 2x2 + 3x3 + 4x4 ≤ 1
    x1, x2, x3, x4 ≥ 0
    2. Maximizar Z = x1 + 2x2 + 3x3
    Sujeta a:
    x1 + 2x2 + x3 ≤ 10
    x1 + x2 ≤ 5
    x1 ≤ 1
    x1, x2, x3 ≥ 0
    3. Maximizar Z = 0,02x1 + 0,10x2 + 0,03x3
    Sujeta a:
    x1 + x2 + x3 ≤ 100 000
    x1 ≤ 60 000
    x2 ≤ 10 000
    x3 ≤ 30 000
    x1, x2, x3 ≥ 0
    4. Maximizar Z = 2x1 + x2 – 3x3 + 5x4
    Sujeta a:
    x1 + 2x2 + 2x3 + 4x4 ≤ 40
    2x1 – x2 + x3 + 2x4 ≤ 8
    4x1 – 2x2 + x3 – x4 ≤ 10
    x1, x2, x3, x4 ≥ 0
    5. Maximizar Z = 8x1 + 6x2 + 3x3 – 2x4
    Sujeta a:
    x1 + 2x2 + 2x3 + 4x4 ≤ 40
    2x1 – x2 + x3 + 2x4 ≤ 8
    4x1 – 2x2 + x3 – x4 ≤ 10
    x1, x2, x3, x4 ≥ 0
    6. Maximizar Z = 3x1 - x2 + 3x3 + 4x4
    Sujeta a:
    x1 + 2x2 + 2x3 + 4x4 ≤ 40
    2x1 – x2 + x3 + 2x4 ≤ 8
    4x1 – 2x2 + x3 – x4 ≤ 10
    x1, x2, x3, x4 ≥ 0
    7. Maximizar Z = 5x1 - 4x2 + 6x3 – 8x4
    Sujeta a:
    x1 + 2x2 + 2x3 + 4x4 ≤ 40
    2x1 – x2 + x3 + 2x4 ≤ 8
    4x1 – 2x2 + x3 – x4 ≤ 10
    x1, x2, x3, x4 ≥ 0
    8. Maximizar Z = 20x1 + 10x2 + x3
    Sujeta a:
    3x1 - 3x2 + 5x3 ≤ 50
    x1 + x3 ≤ 10
    x1 – x2 + 4x3 ≤ 20
    x1, x2, x3, x4 ≥ 0
    9. Maximizar Z = 40x1 + 20x2 + 2x3
    Sujeta a:
    3x1 - 3x2 + 5x3 ≤ 50
    x1 + x3 ≤ 10
    x1 – x2 + 4x3 ≤ 20
    x1, x2, x3, x4 ≥ 0
    10. Maximizar Z = 10x1 + 12x2 - 2x3
    Sujeta a:
    x1 + 2x2 - x3 ≤ 320
    3x1 + x2 ≤ 350
    x3 ≤ 10
    x1, x2, x3 ≥ 0
    11. Maximizar Z = 7x1 + 4x2 + 3x3
    Sujeta a:
    x1 + 2x2 + 2x3 ≤ 30
    2x1 + x2 + 2x3 ≤ 45
    x1, x2, x3, x4 ≥ 0

    12. Maximizar Z = 20 000 x1 + 20 000 x2 + 20 000 x3 + 20 000 x4


    Sujeta a:
    2x1 + x2 + x3 + 2x4 ≤ 24
    2x1 + 2x2 + x3 ≤ 20
    2x3 + 2x4 ≤ 20
    4x4 ≤ 16
    X1, x2, x3, x4 ≥ 0
    13. Maximizar Z = 72x1 + 65x2 + 24x3
    Sujeta a:
    720x1 + 540x2 + 900x3 ≤ 1800
    360x1 + 480x2 + 300x3≤ 1200
    450x1 + 450x2 + 375x3 ≤ 1500
    x1, x2, x3 ≥ 0
    14. Maximizar Z = 6x1 + 5x2 + 4x3
    Sujeta a:
    2x1 + x2 + 3x3 ≤ 180
    x1 + 3x2 + 2x3 ≤ 300
    2x1 + x2 + 2x3 ≤ 240
    x1, x2, x3 ≥ 0
    15. Maximizar Z = 25x1 + 20x2 + 30x3 + 30x4
    Sujeta a:
    3x1 + x2 + 4x3 ≤ 150
    4x1 + 2x2 + 5x3 + 5x4 ≤ 200
    5x1 + 5x2 + 4x3 ≤ 300
    x1, x2, x3, x4 ≥ 0
    16. Maximizar Z = 7x1 + 3x2 + 3x3
    Sujeta a:
    60x1 + 25x2 + 20x3 ≤ 100 000
    50x1 ≤ 60 000
    25x2 ≤ 25 000
    20x3 ≤ 30 000
    x1, x2, x3 ≥ 0
    17. Maximizar Z = 60x1 + 30x2 + 20x3
    Sujeta a:
    8x1 + 6x2 + x3 ≤ 48
    4x1 + 2x2 + 1.5x3 ≤ 20
    2x1 + 1.5x2 + 0.5x3 ≤ 8
    x2 ≤ 5
    x1, x2, x3 ≥ 0
    18. Maximizar Z = x1 + 2x2 + 4x3
    Sujeta a:
    3x1 + x2 + 5x3 ≤ 10
    x1 + 4x2 + x3 ≤ 8
    2x1 + 2x3 ≤ 7
    x1, x2, x3 ≥ 0

    19. Maximizar Z = x1 + 2x2 + 2x3


    Sujeta a:
    5x1 + 2x2 + 3x3 ≤ 15
    x1 + 4x2 + 2x3 ≤ 12
    2x1 + x3 ≤ 8
    x1, x2, x3 ≥ 0

    ING. KARINA REAL A.

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