Question Details

MAT 540
WEEK 10
 
A conditional constraint specifies the conditions under which variables are integers or real variables. 
 
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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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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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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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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 can not be selected.
 
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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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In a __________ integer model, some solution values for decision variables are integers and others can be non-integer.
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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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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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In a 0-1 integer programming model, if the constraint x1-x2 ≤ 0, it means when project 2 is selected, project 1 __________ 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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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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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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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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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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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
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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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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
 
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Consider the following integer linear programming problem 
 
Max Z =      3x1 + 2x2 
Subject to:   3x1 + 5x2 ≤ 30 
                    5x1 + 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
 
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