# Mat 540 Quiz 5

**Topics:**Linear programming, Optimization, Operations research

**Pages:**6 (1011 words)

**Published:**August 27, 2013

Question 1

2 out of 2 points

If exactly 3 projects are to be selected from a set of 5 projects, this would be written as 3 separate constraints in an integer program.

Answer

Selected Answer: False

Correct Answer: False

. Question 2

2 out of 2 points

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

Answer

Selected Answer: False

Correct Answer: False

. Question 3

2 out of 2 points

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

Answer

Selected Answer: True

Correct Answer: True

. Question 4 .2 out of 2 points

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

Answer

Selected Answer: False

Correct Answer: False

. Question 5 .2 out of 2 points

The solution to the LP relaxation of a maximization integer linear program provides an upper bound for the value of the objective function.

Answer

Selected Answer: True

Correct Answer: True

. Question 6 .2 out of 2 points

A conditional constraint specifies the conditions under which variables are integers or real variables.

Answer

Selected Answer: False

Correct Answer: False

. Question 7 .2 out of 2 points

In a __________ integer model, some solution values for decision variables are integers and others can be non-integer. Answer

Selected Answer: mixed

Correct Answer: mixed

. Question 8 .2 out of 2 points

The solution to the linear programming relaxation of a minimization problem will always be __________ the value of the integer programming minimization problem. Answer

Selected Answer: less than or equal to

Correct Answer: less than or equal to

. Question 9 .0 out of 2 points

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

Selected Answer: corequisite

Correct Answer: mutually exclusive

. Question 10 .0 out of 2 points

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

Selected Answer: conditional

Correct Answer: corequisite

. Question 11 .0 out of 2 points

Assume that we are using 0-1 integer programming model to solve a capital budgeting problem and xj = 1 if project j is selected and xj = 0, otherwise. The constraint (x1 + x2 + x3 + x4 ≤ 2) means that __________ out of the 4 projects must be selected. Answer

Selected Answer: exactly 2

Correct Answer: at most 2

. Question 12 .2 out of 2 points

In a 0-1 integer programming model, if the constraint x1-x2 ≤ 0, it means when project 2 is selected, project 1 __________ be selected. Answer

Selected Answer: can sometimes

Correct Answer: can sometimes

. Question 13 .2 out of 2 points

Binary variables are

Answer

Selected Answer: 0 or 1 only

Correct Answer: 0 or 1 only

. Question 14 .2 out of 2 points

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

Selected Answer: conditional

Correct Answer: conditional

. Question 15 .2 out of 2 points

You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or

S4 will prevent you from assessing site S5.

Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, write the constraint(s) for the second restriction...

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