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Circle the correct answer for the following statements. For a max problem, optimal z-value for LP relaxation is lower than optimal z-value for IP. TRUE FALSE An Integer Programming problem is a Linear Programming problem in which all of the variables are required to be non-negative integers. TRUE FALSE Both LP and IP have a convex set. TRUE FALSE Basic feasible solutions of an LP are also the extreme points of the feasible region. TRUE FALSE If an LP has any ? or = constraints, the Big M Method or the Two-phase Simplex Method may be used to solve the problem. TRUE FALSE A constraint is binding if the left-hand side and the right-hand side of the constraint are unequal when the optimal values of the decision variables are substituted into the constraint. TRUE FALSE Feasible region for the IP’s LP relaxation is a subset of feasible region of the IP. TRUE FALSE In relation to a minimization problem, the z-value for the candidate solution obtained from a sup-problem of the B&B algorithm is a lower bound on the optimal z-value for the original IP. TRUE FALSE If any artificial variables are positive in the optimal solution, then the original problem is infeasible. TRUE FALSE There are infinite number of optimal solutions when isoprofit/isocost line leaves the feasible region, it will intersect an entire line segment corresponding to the binding constraint. TRUE FALSE An IP in which all variables are required to be integers is called a pure integer-programming problem. TRUE FALSE A sup-problem of the B&B algorithm related to a maximization problem can be fathomed when it is infeasible or its optimal z value can beat the current LB. TRUE FALSE To solve a mixed IP by the B&B algorithm, branch only on all non-integer variables. TRUE FALSE If we change the rhs value of a constraint, then as long as the point where the binding constraints remains feasible, the optimal solution will still occur where the binding constraints intersect. TRUE FALSE If you solve the LP relaxation of a pure IP and obtain a solution in which all variables are integers, then the optimal solution to the LP relaxation is also the optimal solution to the IP. TRUE FALSE

Circle the correct answer for the following statements.
For a max problem, optimal z-value for LP relaxation is lower than optimal z-value for IP. TRUE FALSE
An Integer Programming problem is a Linear Programming problem in which all of the variables are required to be non-negative integers. TRUE FALSE
Both LP and IP have a convex set. TRUE FALSE
Basic feasible solutions of an LP are also the extreme points of the feasible region. TRUE FALSE
If an LP has any ? or = constraints, the Big M Method or the Two-phase Simplex Method may be used to solve the problem. TRUE FALSE
A constraint is binding if the left-hand side and the right-hand side of the constraint are unequal when the optimal values of the decision variables are substituted into the constraint. TRUE FALSE
Feasible region for the IP’s LP relaxation is a subset of feasible region of the IP. TRUE FALSE
In relation to a minimization problem, the z-value for the candidate solution obtained from a sup-problem of the B&B algorithm is a lower bound on the optimal z-value for the original IP. TRUE FALSE
If any artificial variables are positive in the optimal solution, then the original problem is infeasible. TRUE FALSE
There are infinite number of optimal solutions when isoprofit/isocost line leaves the feasible region, it will intersect an entire line segment corresponding to the binding constraint. TRUE FALSE
An IP in which all variables are required to be integers is called a pure integer-programming problem. TRUE FALSE
A sup-problem of the B&B algorithm related to a maximization problem can be fathomed when it is infeasible or its optimal z value can beat the current LB. TRUE FALSE
To solve a mixed IP by the B&B algorithm, branch only on all non-integer variables. TRUE FALSE
If we change the rhs value of a constraint, then as long as the point where the binding constraints remains feasible, the optimal solution will still occur where the binding constraints intersect. TRUE FALSE
If you solve the LP relaxation of a pure IP and obtain a solution in which all variables are integers, then the optimal solution to the LP relaxation is also the optimal solution to the IP. TRUE FALSE

Added by Kim C.

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