Vikas

MAT540/MAT 540 WEEK 10 QUIZ 1

MAT 540
WEEK 10
 
Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem. 
 
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The solution to the LP relaxation of a maximization integer linear program provides an upper bound for the value of the objective function. 
 
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2 out of 2 points
 
If we are solving a 0-1 integer programming problem with three decision variables, the constraint x1 + x2 + x3 ≤ 3 is a mutually exclusive constraint. 
 
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A conditional constraint specifies the conditions under which variables are integers or real variables. 
 
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If we are solving a 0-1 integer programming problem with three decision variables, the constraint x1 + x2 ≤ 1 is a mutually exclusive constraint. 
 
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If exactly 3 projects are to be selected from a set of 5 projects, this would be written as 3 separate constraints in an integer program. 
 
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If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a __________ constraint.
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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?
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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.
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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.
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Max Z = 5x1 + 6x2 
Subject to: 17x1 + 8x2 ≤ 136 
                  3x1 + 4x2 ≤ 36 
                  x1, x2 ≥ 0 and integer 
What is the optimal solution?
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In a 0-1 integer programming model, if the constraint x1-x2 = 0, it means when project 1 is selected, project 2 __________ be selected.
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If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is
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If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint.
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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.
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If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a __________ constraint.
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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
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Binary variables are
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Max Z =   3x1 + 5x2 
Subject to:      7x1 + 12x2 ≤ 136 
                       3x1 + 5x2 ≤ 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
 
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Consider the following integer linear programming problem 
 
Max Z =      3x1 + 2x2 
Subject to:   3x1 + 5x2 ≤ 30 
                    4x1 + 2x2 ≤ 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 



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17 Dec 2015

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  1. Vikas

    MAT540/MAT 540 WEEK 10 QUIZ 1

    Consider the following integer linear programming problem Max Z = 3x1 + 2x2 Subject to ****** ******
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