Question 1

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

Question 2

If we are solving a 0]1 integer programming problem with three decision variables, theconstraint x1 + x2 + x3 . 3 is a mutually exclusive constraint.

Question 3

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

Question 4

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

Question 5

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

Question 6

If exactly 3 projects are to be selected from a set of 5 projects, this would be written as 3separate constraints in an integer program.

Question 7

Max Z = 5×1 + 6x2Subject to: 17×1 + 8×2 . 1363×1 + 4×2 . 36×1, x2 . 0 and integerWhat is the optimal solution?

Question 8

Assume that we are using 0]1 integer programming model to solve a capital budgeting problemand 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 beselected.

Question 9

If we are solving a 0]1 integer programming problem, the constraint x1 + x2 . 1 is a __________constraint.

Question 10

In a __________ integer model, some solution values for decision variables are integers andothers can be non]integer.

Question 11

If we are solving a 0]1 integer programming problem, the constraint x1 . x2 is a__________ constraint.

Question 12

In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannotbe selected. Which of the alternatives listed below correctly models this situation?

Question 13

You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designateeach 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 orS4 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 14

You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designateeach 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 orS4 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 15

The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoffhas 4 different machines that can produce this kind of hose. Because these machines are fromdifferent manufacturers and use differing technologies, their specifications are not the same.Write the constraint that indicates they can purchase no more than 3 machines.

Question 16

In a 0]1 integer programming model, if the constraint x1]x2 = 0, it means when project 1 isselected, project 2 __________ be selected.

Question 17

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

Question 18

If we are solving a 0]1 integer programming problem, the constraint x1 + x2 = 1 is a __________constraint.

Question 19

Consider the following integer linear programming problemMax Z = 3×1 + 2x2Subject to: 3×1 + 5×2 . 305×1 + 2×2 . 28×1 . 8×1 ,x2 . 0 and integerFind the optimal solution. What is the value of the objective function at the optimalsolution. Note: The answer will be an integer. Please give your answer as an integer without anydecimal point. For example, 25.0 (twenty]five) would be written 25

Question 20

Consider the following integer linear programming problemMax Z = 3×1 + 2x2Subject to: 3×1 + 5×2 . 304×1 + 2×2 . 28×1 . 8×1 , x2 . 0 and integerFind the optimal solution. What is the value of the objective function at the optimalsolution. Note: The answer will be an integer. Please give your answer as an integer without anydecimal point. For example, 25.0 (twenty]five) would be written 25

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