**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 *x*1 + *x*2 ≤ 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 *x*1 ≤ *x*2 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 *x*1 = *x*2 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 *x*1 + *x*2 ≤ 1 is a __________ constraint.

Answer

multiple choice

mutually exclusive

conditional

corequisite

2 points

**Question 17 **

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

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 = 3x_{1} + 5x_{2 }

Subject to: 7x_{1} + 12x_{2} ≤ 136

3x_{1} + 5x_{2} ≤ 36

x_{1}, x_{2} ≥ 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

2 points

**Question 20 **

Consider the following integer linear programming problem

Max Z = 3x_{1} + 2x_{2 }

Subject to: 3x_{1} + 5x_{2} ≤ 30

5x_{1} + 2x_{2} ≤ 28

x_{1} ≤ 8

x_{1} ,x_{2} ≥ 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

**Category:**Mathematics, General Mathematics

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