# Mat 540 Week 9 Quiz 5

Question 1

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

Answer

True

false

2 points

Question 2

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

Answer

True

False

Question 3

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

Answer

True

False

Question 4

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

2 points

Question 5

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

2 points

Question 6

In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 – x2 ≤ 0 implies that if project 2 is selected, project 1 cannot be selected.

Answer

True

False

2 points

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

2 points

Question 8

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

2 points

Question 9

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

Answer

multiple choice

mutually exclusive

conditional

corequisite

2 points

Question 10

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

2 points

Question 11

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

Answer

total

0 – 1

Mixed

all of the above

2 points

Question 12

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

Answer

S2 +S5 ≤ 1

S4 +S5 ≤ 1

S2 +S5 + S4 +S5 ≤ 2

S2 +S5 ≤ 1, S4 +S5 ≤ 1

2 points

Question 13

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

2 points

Question 14

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

2 points

Question 15

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

2 points

Question 16

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

2 points

Question 17

Max Z = 5×1 + 6×2

Subject to: 17×1 + 8×2 ≤ 136

3×1 + 4×2 ≤ 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

2 points

Question 18

In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation?

Answer

x1 + x2 + x5 ≤ 1

x1 + x2 + x5 ≥1

x1 + x5 ≤ 1, x2 + x5 ≤ 1

x1 – x5 ≤ 1, x2 – x5 ≤ 1

2 points

Question 19

Max Z = 3×1 + 5×2

Subject to: 7×1 + 12×2 ≤ 136

3×1 + 5×2 ≤ 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 below

2 points

Question 20

Consider the following integer linear programming problem

Max Z = 3×1 + 2×2

Subject to: 3×1 + 5×2 ≤ 30

5×1 + 2×2 ≤ 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 below