# 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 x1 + x2 ≤ 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 x1 ≤ x2 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 x1 + x2 = 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

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