Applied Stat & Optimization Models 2019 Final Study 1

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

0-1 integer

Which constraint best describes the situation with decision variables A and B? B - A = 0 B + A = 1 B - A ≤ 0 B + A ≤ 1

B - A = 0

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

False

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.

False

The branch and bound solution method cannot be applied to 0-1 integer programming problems.

False

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

True

The divisibility assumption is violated by integer programming

True

The production planner for Airbus showed his boss the latest product mix suggestion from their slick new linear programming model: 12.5 model 320s and 17.4 model 340s. The boss looked over his glasses at the production planner and reminded him that they had several half airplanes from last year's production rusting in the parking lot. No one, it seems, is interested in half of an airplane. The production planner whipped out his red pen and crossed out the .5 and .4, turning the new plan into 12 model 320s and 17 model 340s. This production plan is definitely feasible.

True

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

True

The objective function is

answer with 3 then 4 + 3

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

conditional

If we are solving a 0-1 integer programming problem, the constraint x1 ≤ x2 is a ________ constraint. multiple choice mutually exclusive conditional corequisite

conditional

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 can never can also can sometimes

must also

Obviously if the model wants to upgrade the kitchen, it should be done by either the landlord or a subcontractor. As he creates the IP model, the landlord wants to leave the choice of whether to actually upgrade the kitchen up to the optimization algorithm. How should this constraint be written if he uses the following scheme for decision variables? x3 - x4 = 1 x3 - x4 ≤ 1 x3 + x4 ≤ 1 x3 + x4 = 1

x3 + x4 ≤ 1

Which of these constraints will ensure that a low capacity facility is not built in South America?

y12 + y22 = 0

Which of the constraints best describes the relationship between the iPads for everyone and the speaker series? A - C = 0 A + C = 2 A + C = 1 A - C ≤ 1

A + C = 1

Types of integer programming models are: total. 0-1. mixed. all of the above

All of the above

If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a ________ constraint. multiple-choice mutually exclusive conditional corequisite

Corequisite

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

False

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

False

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

False

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

False

Use the scheme of location (J, C, or G) and excursion (S, P, H, L, Te or Tu) to represent the decision variables. What of these sets of constraints appropriately limits the number of excursions based on the scenario?

JS + JP + JH + JL = 1 CS + CP + CH + CL + CTe = 1 GS + GP + GH + GL + GTu = 1

Assuming that Si is a binary variable, the constraint for the first restriction is: S1 + S3 + S7 ≤1. S1 + S3 + S7 = 2. S1 + S3 + S7 ≥ 1. S1 + S3 + S7 ≤ 2.

S1 + S3 + S7 ≤ 2.

The landlord ran the model in Excel and received the answer report contained in the table. Which of the following statements is correct? The rent will be $180 higher and the project will take 3.5 weeks to finish at a cost of $2900. The rent will be $195 higher and the project will take 3.5 weeks to finish at a cost of $3700. The rent will be $180 higher and the project will take 2.5 weeks to finish at a cost of $3700. The rent will be $195 higher and the project will take 2.5 weeks to finish at a cost of $2900.

The rent will be $180 higher and the project will take 3.5 weeks to finish at a cost of $2900.

In a ________ integer model, all decision variables have integer solution values. total 0-1 mixed all of the above

Total

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.

True

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

True

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

True

The college dean is deciding among three equally qualified (in their eyes, at least) candidates for his associate dean position. If this situation could be modeled as an integer program, the decision variables would be cast as 0-1 integer variables.

True

The constraint for the North American supply region is:

X11 + X12 + X13 + X14 - 5Y11 - 10Y12 ≤ 0

The constraint for the South Asia demand region is:

X13 + X23 + X33 + X43 = 7.

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

continuous

In an integer program, if we were choosing between two locations to build a facility, this would be written as:

x1 + x2 = 1

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 + x2 + x5 ≤ 1 x1 - x5 ≤ 1, x2 - x5 ≤ 1 x1 + x5 ≤ 1, x2 + x5 ≤ 1 x1 + x2 + x5 ≥ 1

x1 + x5 ≤ 1, x2 + x5 ≤ 1

Which of these formulations of the budget constraint is correct? Assume that there are 20 students in this semesters MBA class. A + B + C + D + E ≤ 20 $15,000A + $500B + $15,000C + $200D + $100E ≤ $56,250 $750A + $25B + $15,000C + $10D + $5E ≤ $56,250 20A + 20B + C + 20D + 20E ≤ $56,250

$15,000A + $500B + $15,000C + $200D + $100E ≤ $56,250

In a ________ integer model, the solution values of the decision variables are 0 or 1. total 0-1 mixed all of the above

0-1

_______ variables are best suited to be the decision variables when dealing with yes-or-no decisions.

0-1

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. optimally always never sometimes

Always

Which constraint is most appropriate if the students can choose only three of these activities?

E + S +L + B ≤ 3

What is an appropriate objective function for this vacation? Max Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP + 3GH + 1GL + 3GTu Max Z = JS + JP + JH + JL + CS + CP + CH + CL + CTe + GS + GP + GH + GL + GTu Min Z = 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu Min Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP + 3GH + 1GL + 3GTu

Max Z = 3JS + 1JP + 2JH + 3JL + 2CS + 3CP + 1CH + 2CL + 3CTe + 1GS + 2GP + 3GH + 1GL + 3GTu

In all the excitement of waving to the longshoremen as the ship leaves the Port of New Orleans, the management scientist drops his wallet in the Mississippi River. Rather than maximize enjoyment for the three excursions, he must now adjust his model to select three inexpensive options. Which combinations of objective function and constraints are best if the scheme of location (J, C, or G) and excursion (S, P, H, L, Te or Tu) is used to represent the decision variables?

Min Z = 100JS + 95JP + 120JH + 60JL + 110CS + 55CP + 70CH + 90CL + 130CTe + 90GS + 60GP + 110GH + 130GL + 95GTu subject to: JS + JP + JH + JL = 1 CS + CP + CH + CL + CTe = 1 GS + GP + GH + GL + GTu = 1

A ________ integer model allows for the possibility that some decision variables are not integers.

Mixed

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.

Mixed Integer

The constraint for distribution center 1 is: X11 + X12 + X13 + X14 ≤ 500. X11 + X12 + X13 + X14 ≥ 500. X11 + X12 + X13 + X14D + 500y1 ≤ 0. X11 + X12 + X13 + X14 - 500y1 ≤ 0.

X11 + X12 + X13 + X14 - 500y1 ≤ 0.

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 never must always is already can sometimes

can sometimes

"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."

mixed or mutually exclusive

If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is: never optimal and feasible. always feasible. always optimal and feasible. sometimes optimal and feasible.

sometimes optimal and feasible.

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. always, non-optimal never, non-optimal always, optimal sometimes, optimal

sometimes, optimal

Max Z = 5x1 + 6x2 Subject to: 17x1 + 8x2 ≤ 136 3x1 + 4x2 ≤ 36 x1, x2 ≥ 0 and integer What is the optimal solution? x1 = 2, x2 = 6, Z = 46 x1 = 3, x2 = 6, Z = 51 x1 = 6, x2 = 4, Z = 54 x1 = 4, x2 = 6, Z = 56

x1 = 4, x2 = 6, Z = 56

Which of these constraints would not be appropriate for this scenario? 2700x1 + 400x2 + 2500x3 + 1000x4 + 600x5 + 250x6 + 350x7 + 400x8 ≤ 3000 x3 + x4 = 1 1x1 + 2x2 + 1.5x3 + 3x4 + 0.5x5 + 1x6 + 0.25x7 + 0.5x8 ≤ 4 x1, x2, x3, x4, x5, x6 , x7, x8 ≥ 0 and integer

x1, x2, x3, x4, x5, x6 , x7, x8 ≥ 0 and integer

Suppose the landlord really wants the back door to be installed. For too long he has had to cut through the garage and he figures when he retires, this house will be a perfect downsize home for him to move into. How should the constraint for the back door be written if he uses the following scheme for decision variables? x5 + x6 ≤ 1 x5 - x6 ≤ 1 x5 - x6 = 1 x5 + x6 = 1

x5 + x6 = 1