MAT 540 Quiz 5

Question 1

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

 True

 False

Question 2

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

Answer

 True

 False

Question 3

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

Answer

 True

 False

Question 4

In a mixed integer model, some solution values for decision variables are integer and others are only 0 or 1.

Answer

 True

 False

Question 5

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

 True

 False

Question 6

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

Answer

 True

 False

Question 7

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

Answer

multiple choice

mutually exclusive

conditional

corequisite

Question 8

Max Z = 5x1 + 6x2

Subject to: 17x1 + 8x2 ≤ 136

                  3x1 + 4x2 ≤ 36

x1, x2 ≥ 0 and integer

What is the optimal solution?

Answer

x1 = 6, x2 = 4, Z = 54

x1 = 3, x2 = 6, Z = 51

x1 = 2, x2 = 6, Z = 46

x1 = 4, x2 = 6, Z = 56

Question 9

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

exactly 2

at least 2

at most 2

none of the above

Question 10

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

Answer

greater than or equal to

less than or equal to

equal to

different than

Question 11

Binary variables are

Answer

0 or 1 only

any integer value

any continuous value

any negative integer value

Question 12

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

must always

can sometimes

can never

A and B

Question 13

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

Answer

multiple choice

mutually exclusive

conditional

corequisite

Question 14

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, the constraint for the first restriction is

Answer

S1 + S3 + S7 ≥ 1

S1 + S3 + S7 ≤1

S1 + S3 + S7 = 2

S1 + S3 + S7 ≤ 2

Question 15

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

Answer

multiple choice

mutually exclusive

conditional

corequisite

Question 16

The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same.

Write the constraint that indicates they can purchase no more than 3 machines.

Answer

Y1 + Y2 + Y3+ Y4 ≤ 3

Y1 + Y2 + Y3+ Y4 = 3

Y1 + Y2 + Y3+ Y4 ≥3

none of the above

Question 17

If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is

Answer

always optimal and feasible

sometimes optimal and feasible

always optimal but not necessarily feasible

never optimal and feasible

Question 18

The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same.

Write a constraint to ensure that if machine 4 is used, machine 1 will not be used.

Answer

Y1 + Y4 ≤ 0

Y1 + Y4 = 0

Y1 + Y4 ≤ 1

Y1 + Y4 ≥ 0

Question 19

Max Z =   3x1 + 5x2

Subject to:      7x1 + 12x2 ≤ 136

                       3x1 + 5x2 ≤ 36

x1, x2 ≥ 0 and integer

Find the optimal solution. What is the value of the objective function at the optimal solution. Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty-five) would be written 25

Answer

Question 20

Consider the following integer linear programming problem

Max Z =      3x1 + 2x2

Subject to:   3x1 + 5x2 ≤ 30

                    5x1 + 2x2 ≤ 28

x1 ≤ 8

x1 ,x2 ≥ 0 and integer

Find the optimal solution. What is the value of the objective function at the optimal solution. Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty-five) would be written 25

Answer