# mathematics

Question-1:

In a problem involving capital budgeting applications, the 0-1variables designate the acceptance or rejection of the different projects.

True

False

Question-2:

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.

True

False

Question-3:

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

True

False

Question-4:

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

True

False

Question-5:

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

True

False

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.

True

False

Question-7:

If we are solving a 0-1 integer programming problem, the constraint *x*1 ≤ *x*2 is a __________ constraint.

Question-8:

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

Question-9:

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.

Question-10:

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

Question-11:

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.

Machine | Fixed Cost to Setup Production Run | Variable Cost per Hose | Capacity |

1 | 750 | 1.25 | 6000 |

2 | 500 | 1.50 | 7500 |

3 | 1000 | 1.00 | 4000 |

4 | 300 | 2.00 | 5000 |

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

Question-12:

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

Question-13:

Subject to: 17×1 + 8×2 ≤ 136

3×1 + 4×2 ≤ 36

x1, x2 ≥ 0 and integer

What is the optimal solution?

Question-14:

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

Question-15:

If we are solving a 0-1 integer programming problem, the constraint *x*1 + *x*2 = 1 is a __________ constraint.

Question-16:

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

Question-17:

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.

Machine | Fixed Cost to Setup Production Run | Variable Cost per Hose | Capacity |

1 | 750 | 1.25 | 6000 |

2 | 500 | 1.50 | 7500 |

3 | 1000 | 1.00 | 4000 |

4 | 300 | 2.00 | 5000 |

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

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?

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 (twentyfive)*

*would be written 25*

* *

Question-20:

Consider the following integer linear programming problem

Max Z = 3×1 + 2×2

Subject to: 3×1 + 5×2 ≤ 30

4×1 + 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 (twentyfive)*

*would be written 25*