It converts every integer linear program into a shortest path problem.

It systematically partitions the problem and uses bounds to discard subproblems that cannot improve the current best solution.

It guarantees a feasible solution by ignoring integrality constraints.

It solves only minimization problems with two variables.

A complete graph, because every node must connect to every other node.

A directed graph, because each arc has an orientation.

An undirected graph, because direction is irrelevant in all road systems.

A tree, because cycles are forbidden in city street networks.

The reduced costs of a simplex tableau only.

The names of the players but not their strategies.

The outcome or payoff associated with each combination of strategies.

The list of all graph edges without any numerical values.

Only node colors, because capacities are not needed in flow models.

Arc capacities, along with a designated source node and sink node.

Only the total number of nodes, because arcs do not affect flow.

Only whether the graph is planar.

$145

$75

$650

$195

Greedy heuristic

Constraint programming

Integer linear programming

Linear programming

Neither maximizing profit nor the machine-hour limit belongs in the model.

Both maximizing profit and the machine-hour limit are objectives.

The 500 machine-hour limit is the objective, and maximizing profit is a constraint.

Maximizing profit is the objective, and the 500 machine-hour limit is a constraint.

Because origins, destinations, costs, supplies, and demands can be organized clearly in rows and columns.

Because matrix form eliminates the need for supply and demand constraints.

Because transportation models cannot be represented in any other way.

Because matrix form automatically proves optimality without computation.

Minimize the sum over i of c_i + e_i + x_i

Minimize the sum over i of (c_i + e_i)x_i

Minimize the sum over i of c_i e_i x_i^2

Maximize the sum over i of (c_i - e_i)x_i

Because a graph makes connectivity, paths, neighborhoods, and network structure explicit.

Because graphs can represent only complete networks.

Because a graph automatically solves the optimization problem without an algorithm.

Because graphs eliminate the need to define nodes and edges.