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# Branch and bound solution of problem

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Max z= 7x1+3x2
2x1+x2<=9
3x1+2x2<=13

x1,x2>=0
x1,x2 integer

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Branch and bound solution of problem is presented.

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Branch and bound solution of problem
Max z= 7x1+3x2
2x1+x2<=9
3x1+2x2<=13

x1,x2>=0
x1,x2 integer

First solve the LP relaxation of the problem, which is the root.
(0) Max z= 7x1+3x2
2x1+x2<=9
3x1+2x2<=13

x1,x2>=0

The optimal solution is (x1, x2)=(13/3, 0) with objective value = 91/3. So 91/3=30.333 is the upper bound of the IP solution. It is not the optimal solution to IP because x1 is fractional.
So we branch on x1 =13/3=4.333 by creating two sub-problems. Sub-problem (1) is by adding x1<=4 to the root. Sub-problem (2) is by adding x1>=5 to the root. Remember that we cannot include the LP ...

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