Exam 5: Integer Programming

The divisibility assumption is violated by integer programming.

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 -What is a full set of constraints for this problem if there are 30 MBA students enrolled this semester?

"It's me or the cat!" the exasperated husband bellowed to his well-educated wife. "Hmmmm," she thought, "I could model this decision with a ________ constraint."

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

In a ________ integer model, all decision variables have integer solution values.

The Wiethoff Company has a contract to produce 10,000 garden hoses for a customer. Wiethoff has four 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. Machine Fixed Cost to Setup Production Run Variable Cost per Hose Capacity 1 750 1.25 6000 2 500 1.50 7500 3 1000 1.00 4000 4 300 2.00 5000 -Write the constraint for machine 4.

A conditional constraint specifies the conditions under which variables are integers or real variables.

If exactly one investment is to be selected from a set of five investment options, then the constraint is often called a ________ constraint.

One type of constraint in an integer program is a multiple-choice constraint.

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.

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.

A feasible solution to an integer programming problem is ensured by rounding down non-integer solution values.

Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem.

In a ________ linear programming model, some of the solution values for the decision variables are required to assume integer values and others can be integer or noninteger.

In a ________ linear programming model, the solution values of the decision variables are zero or one.

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

In a mixed integer model, all decision variables have integer solution values.

Rounding down integer solution values ensures an infeasible solution to an integer linear programming problem.

The Wiethoff Company has a contract to produce 10,000 garden hoses for a customer. Wiethoff has four 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. Machine Fixed Cost to Setup Production Run Variable Cost per Hose Capacity 1 750 1.25 6000 2 500 1.50 7500 3 1000 1.00 4000 4 300 2.00 5000 -Write the constraint the indicates they can purchase no more than three machines.

In the classic game show Password, the suave, silver-haired host informed the contestants, "you can choose to pass or to play." This expression suggests a mixed integer model is most appropriate.