# Integer Linear Programming and Optimal Solution

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1. Consider the following integer linear programming problem.

Max Z = 3x1 + 2x2

Subject to: 3x1 + 5x2 <= 30

4x1 + 2x2 <= 28

x1 <= 8

x1, x2 >= 0 and integer

The solution to the linear programming relaxation is: x1 = 5.714, x2= 2.571.

What is the optimal solution to the integer linear programming problem? State the value of the objective function Z = x or x.x.

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#### Solution Preview

1. Consider the following integer linear programming problem.

Max Z = 3x1 + 2x2

Subject to: 3x1 + 5x2 <= 30

4x1 + 2x2 <= 28

x1 <= 8

x1, x2 >= 0 and integer

The solution to the linear ...

#### Solution Summary

This solution contains a detailed explanation of solving an integer linear programming problem.

$2.49