Question 1

A rounded-down integer solution can result in a less than optimal solution to an integer programming problem.

Accepted Answer

When rounding down, it is possible to miss the optimal solution, as the rounded-down integer may not always be the closest integer to the optimal solution. This can lead to a suboptimal or less than optimal solution.

Question 2

Rounding non-integer solution values up to the nearest integer value will still result in a feasible solution.

Accepted Answer

Rounding non-integer solution values up to the nearest integer value may result in a value that violates some constraints or objective function, thus resulting in an infeasible solution.

Question 3

The ________ method is based on the principle that the total set of fesible solutions can be partitioned into smaller subsets of solutions.

Accepted Answer

The answer of The ________ method is based on the...

Question 4

"It's me or the cat!" the exasperated husband bellowed to his well-educated wife. "Hmmmm," she thought, "I could model this decision with a ________ constraint."

Accepted Answer

The answer of "It's me or the cat!" the exasperated...

Question 5

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 + x3 ≤ 3 is a mutually exclusive constraint.

Accepted Answer

A mutually exclusive constraint typically requires that out of a set of variables, only one can take the value 1 (or be "chosen") at a time, implying a constraint of the form x1 + x2 + x3 ≤ 1. The given constraint x1 + x2 + x3 ≤ 3 allows for the possibility of more than one variable being 1 simultaneously, as long as their sum does not exceed 3.

Question 6

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a conditional constraint.

Accepted Answer

This is a conditional constraint as it imposes a condition that if x1 takes a value of 1, then x2 must also take a value of 1 or greater.

Question 7

In a ________ integer programming model, a solution of x2 = 7 is not possible.

Accepted Answer

The answer of In a ________ integer programming model, a...

Question 8

In a ________ linear programming model, the solution values of the decision variables are zero or one.

Accepted Answer

The answer of In a ________ linear programming model, the...

Question 9

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint.

Accepted Answer

In a 0-1 integer programming problem, the constraint x1 = x2 is a linear equality constraint, not a conditional constraint, because it directly specifies a relationship between variables without any conditions.

Question 10

In a ________ linear programming model, some of the solution values for the decision variables are required to assume integer values and others can be integer or noninteger.

Accepted Answer

The answer of In a ________ linear programming model, some...

Question 11

Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem.

Accepted Answer

Rounding non-integer solution values to the nearest integer may or may not result in an infeasible solution; it depends on the specific constraints and structure of the integer linear programming problem.

Question 12

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a mutually exclusive constraint.

Accepted Answer

A mutually exclusive constraint means that the variables involved cannot take on values that satisfy the constraint simultaneously. In this case, if x1 takes on a value of 1, then x2 must be equal to 0 in order for the constraint to be satisfied. Therefore, x1 and x2 are mutually exclusive values under this constraint.

Question 13

Rounding down integer solution values ensures an infeasible solution to an integer linear programming problem.

Accepted Answer

Rounding down integer solution values does not ensure an infeasible solution to an integer linear programming problem; it may still result in a feasible solution, although not necessarily the optimal one.

Question 14

If exactly one investment is to be selected from a set of five investment options, then the constraint is often called a ________ constraint.

Accepted Answer

The answer of If exactly one investment is to be...

Question 15

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a mutually exclusive constraint.

Accepted Answer

A mutually exclusive constraint means that the variables involved cannot take on values that satisfy the constraint simultaneously. In this case, if x1 takes on a value of 1, then x2 must be equal to 0 in order for the constraint to be satisfied. Therefore, x1 and x2 are mutually exclusive values under this constraint.

Question 16

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a mutually exclusive constraint.

Accepted Answer

The constraint x1 ≤ x2 is not a mutually exclusive constraint as it allows for the possibility that x1 and x2 can both be equal to 0 or 1 simultaneously. A mutually exclusive constraint would be something like x1 + x2 ≤ 1, which would restrict x1 and x2 from both taking the value of 1 at the same time.

Question 17

An optimal solution to an integer programming problem is ensured by rounding down non-integer solution values.

Accepted Answer

Rounding down non-integer solution values may not necessarily give an optimal solution in all cases.

Question 18

In choosing four electives from the dazzling array offered by the Decision Sciences Department next semester, the students that had already taken the management science class were able to craft a model using a ________ constraint.

Accepted Answer

The answer of In choosing four electives from the dazzling...

Question 19

A ________ integer model allows for the possibility that some decision variables are not integers.

Accepted Answer

The answer of A ________ integer model allows for the...

Question 20

If we graph the problem that requires x1 and x2 to be an integer, it has a feasible region consisting of ________.

Accepted Answer

The answer of If we graph the problem that requires...

Quiz 5: Integer Programming