Question

Consider the following integer programming problem.Maximize:
z=8x_{1} +12x_{2} +6x_{3}
+4x_{4}

Subject to constraint: 5x_{1} + 9x_{2}
+4x_{3} +3x_{4} ≤ 16 where x1, x2, x3 and x4 are
binary integers (0 or 1).

**By applying the Branch and Bound Algorithm find the
solution.**

Answer #1

**Solution:**

Assume, ,,,

The Equation will be satisfied as below

To maximise

Sustitute above values in Z

i.e.

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Solve for all 4-tuples (x1, x2, x3, x4) simultaneously
satisfying the following equations:
8x1 −9x2 −2x3 −5x4 = 100
9x1 +6x2 −6x3 +9x4 = 60
−3x1 −9x2 +4x3 −2x4 = −52
−7x2 +8x3 +8x4 = −135

** Linear Programming
**
Max Z = 6x1 +
10x2+9x3 + 20x4
constraint
4x1 + 9x2 + 7x3 + 10x4
= 600
x1 + x2+3x3 + 40x4=
400
3x1 + 4x2 + 2x3 + x4 =
500
x1,x2,x3 ,x4 ≥ 0
Find the allowable decrease
and increase for x4.

The following is the mathematical model of a linear programming
problem for profit:
Maximize subject to
Z = 2X1 + 3X2
4X1+9X2 ≤ 72 10X1 + 11X2 ≤ 110 17X1 + 9X2 ≤ 153
X1 , X2 ≥ 0
The constraint lines have been graphed below along with one
example profit line (dashed). The decision variable X1 is used as
the X axis of the graph. Use this information for questions
19 through 23.
A). Which of the following gives...

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