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7 November, 16:59

Find all optimal solutions to the following LP using the Simplex Algorithm:

maxz = x1 + 2x2 + 3x3

s. t.

x1 + 2x2 + 3x3 ≤ 10

x1 + x2 ≤ 5

x1 ≤ 1

x1, x2, x3 ≥ 0

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Answers (1)
  1. 7 November, 20:05
    0
    z=10

    x1=0

    x2=0

    x3=3.33

    Step-by-step explanation:

    First Step convert your constraints in standard equations

    so we have

    x1 + 2x2 + 3x3+x4 = 10

    x1 + x2 + x5 = 5

    x1 + x6 = 1

    Now we pass it all to the simplex table

    Remember that we choose the column with the most negative value

    Pivot Element=3

    Divide all elements on Pivot Line by Pivot Element

    Line x5 = 0*Pivot Line + Line x5

    Line x6 = 0*Pivot Line + Line X6

    Line Z = 3 * Pivot Line + Line Z

    We finish when all the elements from the line Z are positive

    Hence we have that x3=3.33 and x1=0, x2=0 and the max of z is 10
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