a) Consider the following binary integer programing (BIP) problem: Minimize z = 5x₁ + 6x₂ + 7x3 + 8x4 +9x5 subject to 3x₁x2 + x3 + x₁-2x522 x₁ + 3x2-x3-2x4+xs 20 -x₁-x₂ + 3x3 + x + xs ≥ 1 X1, X2, X3, X4, X5 = 0 or 1, Use the BIP branch and bound (B&B) algorithm and draw the trees of sub-problems used in finding the solution.

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a) Consider the following binary integer programing (BIP) problem:
Minimize z = 5x₁ + 6x₂ + 7x3 + 8x4 + 9x5
subject to
3x₁x2 + x3 + x4-2x522
x₁ + 3x2-x3-2x4+x5 20
-x₁x₂ + 3x3 + x4 + X5 2 1
X₁, X2, X3, X4, X5 = 0 or 1,
Use the BIP branch and bound (B&B) algorithm and draw the trees of sub-problems used in finding the
solution.
Transcribed Image Text:a) Consider the following binary integer programing (BIP) problem: Minimize z = 5x₁ + 6x₂ + 7x3 + 8x4 + 9x5 subject to 3x₁x2 + x3 + x4-2x522 x₁ + 3x2-x3-2x4+x5 20 -x₁x₂ + 3x3 + x4 + X5 2 1 X₁, X2, X3, X4, X5 = 0 or 1, Use the BIP branch and bound (B&B) algorithm and draw the trees of sub-problems used in finding the solution.
Expert Solution
Step 1

The given LPP is as follows:

Min Z =   5 x1 + 6 x2 + 7 x3 + 8 x4 + 9 x5
subject to
  3 x1 -   x2 +   x3 +   x4 - 2 x5 2
    x1 + 3 x2 -   x3 - 2 x4 +   x5 0
-   x1 -   x2 + 3 x3 +   x4 +   x5 1
and x1,x2,x3,x4,x50;
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