Question

Solve the following integer linear programming problem:
Max 2x1 + 5x2 + 7x3

Subject to,
4x1 + 3x2 + x3 ≥ 29

Where x1, x2, x3 are non-negative integers.

Answer 1

Answer on Question 66367 - Math - Statistics and Probability

Question: Solve the following integer linear programming problem: maximize

$2x_{1}+5x_{2}+7x_{3}$

subject to the constrain $4x_{1}+3x_{2}+x_{3}\geq 29$, where $x_{1}$, $x_{2}$, $x_{3}$ are non-negative integers.

Solution: An integer linear programming problem (ILP) is a linear programming problem (LP) in which some or all of the variables are restricted to be integers. If LP admits an integer solution, then this solution is a solution of ILP. Otherwise, we must apply some special algorithms such as the branch-and-bound algorithm. However if LP is unbounded, then ILP is also unbounded.

Recall that a problem is unbounded if it has feasible solutions with arbitrarily large objective values. The problem under consideration is unbounded. In fact, for the sequence of feasible solutions $X_{n}=(n,0,0)$, where $n=8,9,\dots$ the objective value $2n$ goes to infinity as $n\to+\infty$.

Answer: The problem is unbounded.

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