BUS 560 ch 5

In formulating a mixed integer programming problem, the constraint x1 + x2 ≤ 500y1 where y1 is a 0-1 variable and x1 and x2 are continuous variables, then x1 + x2 = 500 if y1 is:

1.

Saba conducts regular tours of his favorite city in the world, Paris. Each semester he selects among the finest students in the university and escorts them to the City of Lights. In addition to a world-class education on conducting business in Europe, he arranges a number of cultural outings for them to help them immerse themselves in all that France has to offer. He collects an extra $100 from each student for this purpose and limits his tour group to ten lucky individuals. Some of the events (and their prices) he proposes to the students include:Eiffel Tower visit, $40 per student, EParis Sewer spelunking, $20 per student, SHalf day passes to the Louvre, $60 per student, LBon Beret tour, $50 per student, BSo much to do and so little time!Which constraint is most appropriate if the students can choose only three of these activities?

E + S + L + B ≤ 3

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: Select one:

S1 + S3 + S7 ≤ 2.

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.

S2 + S5 ≤ 1, S4 + S5 ≤ 1

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a feasible solution to the integer linear programming problem.

always

In a 0-1 integer programming model, if the constraint x1 - x2 ≤ 0, it means when project 2 is selected, project 1 ________ be selected.

can sometimes

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a ________ constraint.

conditional

Which of the following is not an integer linear programming problem?

continuous

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a ________ constraint.

corequisite

For a maximization integer linear programming problem, a feasible solution is ensured by rounding ________ non-integer solution values if all of the constraints are the less-than-or-equal-to type.

down

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 ________ projects must be selected.

exactly 2, 4

In a 0-1 integer programming model, if the constraint x1 - x2 = 0, it means when project 1 is selected, project 2 ________ be selected.

must also

If we are solving a 0-1 integer programming problem, the constraint x1 + x2 ≤ 1 is a ________ constraint.

mutually exclusive

If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a(n) ________ solution to the integer linear programming problem.

sometimes, optimal

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?

x1 + x5 ≤ 1, x2 + x5 ≤ 1

Max Z = 5x1 + 6x2Subject to: 17x1 + 8x2 ≤ 1363x1 + 4x2 ≤ 36x1, x2 ≥ 0 and integerWhat is the optimal solution?

x1 = 4, x2 = 6, Z = 56

Max Z = 13x1 + 8x2Subject to: 15x1 + 12x2 ≤ 1447x1 + 9x2 ≤ 64x1, x2 ≥ 0 and integerWhat is the optimal solution?

x1 = 9, x2 = 0, Z = 117