1. The complementary slackness principle states that either there is zero slack on a constraint or the reduced cost is zero.
2. An extreme point is always an optimal solution.
3. A map of the United States can be drawn as a network with each state represented by a node and arcs connecting each pair of states that share a boundary.
4. If a general linear programming problem can also be formulated as a network problem, the network formulation is generally preferable because of easier model input and a quicker solution technique.
5. If two extreme points are optimal, then so is every point on the line segment connecting the two extreme points.
6. When specifying linear constraints, the modeler must take into account the unit specification of the decision variables so that the units represented by the left side of the constraints are consistent with the units represented by the right side of the constraints.
7. It takes two pounds of steel and three pounds of copper to make a particular product. If there are 100 pounds of steel and 100 pounds of cooper available, one constraint will be 2X1 + 3X2 <200.
8. The objective function coefficient for X1 is currently $18 and for X2 is $29, and the ranges of optimality for these coefficients are between $15 and $20 and between $25 and $35, respectively. If the objective function coefficients for X1 and X2 simultaneously decline by $2 each, since both coefficients are still within their ranges of optimality, the optimal solution is guaranteed to remain the same.