MAT 540 WEEK 10 A conditional constraint specifies the conditions under which variables are integers or real variables. Answer The solution to the LP relaxation of a maximization integer linear program provides an upper bound for the value of the objective function. Answer Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem. Answer 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. Answer 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. Answer 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. Answer In a __________ integer model, some solution values for decision variables are integers and others can be non-integer. Answer If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a __________ constraint. Answer If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint. Answer 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. Answer In a 0-1 integer programming model, if the constraint x1-x2 ≤ 0, it means when project 2 is selected, project 1 __________ be selected. Answer If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a __________ constraint. Answer 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? Answer 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 Answer 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. Answer Max Z = 5×1 + 6×2 Subject to: 17×1 + 8×2 ≤ 136 3×1 + 4×2 ≤ 36 x1, x2 ≥ 0 and integer What is the optimal solution? Answer 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 Answer If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is Answer 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 (twenty-five) would be written 25 Answer Consider the following integer linear programming problem Max Z = 3×1 + 2×2 Subject to: 3×1 + 5×2 ≤ 30 5×1 + 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 (twenty-five) would be written 25 Answer Mathematics Assignment Help Mathematics Homework help, Mathematics Study Help Mathematics, Course Help
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