Exam 5: Integer Programming

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

In a ________ integer programming model, a solution of x2 = 7 is not possible.

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

The Exorbitant Course Fees. The $75 per credit hour course fee tacked on to all the MBA classes has generated a windfall of $56,250 in its first semester. "Now we just need to make sure we spend it all," the Assistant Dean cackled. She charged the Graduate Curriculum Committee with generating a shopping list before their next meeting. Four months later, the chairman of the committee distributed the following. As the professor for the quantitative modeling course, he tended to think in terms of decision variables, so he added the left-most column for ease of use. Decision Variable Item Cost Note A iPads for everybody \ 750/ unit Must get a cover if these are purchased B iPad covers with MBA logo \ 25/ unit Not needed unless we buy iPads C Speaker series \ 15,000 Can't afford both this and the iPads D Subscriptions to the Wall Street Joumal \ 10/ unit Don't need if we have the electronic version Subscriptions to the electronic version of the Wall E Street Joumal \5 /unit Worthless without the iPads -Which of the following constraints best describes the relationship between the electronic Wall Street Journal subscription and the iPads?

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

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.

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 cannot be selected.

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

Binary variables are

The three types of integer programming models are total, 0-1, and mixed.

Max Z =   x1 + 6x2 Subject to: 17x1 + 8x2 ? 136      3x1 + 4x2 ? 36     x1, x2 ? 0 and integer Find the optimal solution.

If we graph the problem that requires x1 and x2 to be an integer, it has a feasible region consisting of ________.

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, E Paris Sewer spelunking, $20 per student, S Half day passes to the Louvre, $60 per student, L Bon Beret tour, $50 per student, B So much to do and so little time! -The tour group has three days remaining in Paris and the opportunity to do three cultural events. It is important to soak up as much culture as possible, so Saba decides to model this as a 0-1 integer program mandating that the group does three events. A couple of students object, not to the integer program, but to the set of cultural events that they have to choose from. They would rather have the option to do up to three events but perhaps only one or two and spend the rest of their time doing some "retail benchmarking." What was Saba's original constraint and how does that constraint change to cater to the whims of the students?

Consider a capital budgeting example with five projects from which to select. Let x1 = 1 if project a is selected, 0 if not, for a = 1, 2, 3, 4, 5. Projects cost $100, $200, $150, $75, and $300, respectively. The budget is $450. -Write the appropriate constraint for the following condition: If project 1 is chosen, project 5 must not be chosen.

The ________ method is based on the principle that the total set of fesible solutions can be partitioned into smaller subsets of solutions.

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.

In a ________ integer model, some solution values for decision variables are integers and others can be non-integer.

The branch and bound method of solving linear integer programming problems is

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

In a ________ integer model, the solution values of the decision variables are 0 or 1.