# Solve the following problem using the branch and bound technique Max Z= 3×1 + 2×2 sub to 8×1 +16×2 + 4×3 < = 490 20x1 + 12x2 <= 600 x1, x2, x3 > = 0 and integer.

Using the solver and putting the condition on all Decision Variable must be integer:
18 20 0 Objective 94
x1 x2 x3
3 2 0
8 16 4 464 <= 490 20 12 0 600 <= 600 Solution x1= 18 x2= 20 x3 = 0 while with no integer constraint: 16.60714 22.32143 0 Objective 94.46429 x1 x2 x3 3 2 0 8 16 4 490 <= 490 20 12 0 600 <= 600 Objective Cell (Max) Cell Name Original Value Final Value \$F\$2 Objective 94 94.46428571 Variable Cells Cell Name Original Value Final Value Integer \$B\$2 18 16.60714286 Integer \$C\$2 20 22.32142857 Integer \$D\$2 0 0 Integer Constraints Cell Name Cell Value Formula Status Slack \$E\$5 Objective 490 \$E\$5<=\$G\$5 Binding 0 \$E\$6 Objective 600 \$E\$6<=\$G\$6 Binding 0 \$B\$2:\$D\$2=Integer

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