Question 1

The linear program that results from dropping the integer requirements for the variables in an integer linear program is known as

Accepted Answer

A) convex hull. 
B) a mixed-integer linear program. 
C) LP relaxation. 
D) a binary integer linear program.

Question 2

The optimal solution to the integer linear program will be an extreme point of the

Accepted Answer

A) convex hull. 
B) objective contour. 
C) cutting plane. 
D) slope.

Question 3

An apparel designing company is planning to enter the women's trousers market. They are in the process of developing a product that will appeal most to customers. In an integer programming model for this problem, the available sizes of the trousers will be represented as

Accepted Answer

A) binary variables. 
B) constraints. 
C) attributes. 
D) regression constants.

Question 4

The __________ approach to solving integer linear optimization problems breaks the feasible region of the LP Relaxation into subregions until the subregions have integer solutions or it is determined that the solution cannot be in the subregion.

Accepted Answer

A) cutting plane 
B) trial-and-error 
C) breaking region 
D) branch-and-bound

Question 5

__________ constraint is a constraint requiring that two binary variables be equal and that thus are both either in or out of the solution together.

Accepted Answer

A) Conditional 
B) Corequisite 
C) k out of n alternatives 
D) Mutually exclusive

Question 6

The objective function for an optimization problem is: Max 5x - 3y, with constraints x ≥ 0, y ≥ 0 and y must be an integer. x and y are the only decisions variables. This is an example of a(n)

Accepted Answer

A) all-integer linear program. 
B) mixed-integer linear program. 
C) LP relaxation of the integer linear program. 
D) binary integer linear program.

Question 7

In a production application involving a fixed setup cost and a variable cost, the use of __________ makes including the setup cost possible in a production model.

Accepted Answer

A) location variables 
B) noninteger constraints 
C) objective function coefficients 
D) binary variables

Question 8

An apparel designing company is planning to enter the women's trousers market. They are in the process of developing a product that will appeal most to customers. Pink, green, and black will be __________ of the color attribute.

Accepted Answer

A) levels 
B) constraints 
C) regression constants 
D) utility values

Question 9

A binary mixed-integer programming problem in which the binary variables represent whether an activity, such as a production run, is undertaken or not is known as the

Accepted Answer

A) capital budgeting problem. 
B) share of choice problem. 
C) fixed-cost problem. 
D) covering problem.

Question 10

__________ analysis is a market research technique that can be used to learn how prospective buyers of a product value the product's attributes.

Accepted Answer

A) Part-worth 
B) Conjoint 
C) Regression 
D) Sensitivity

Question 11

The __________ of a set of points is the smallest intersection of linear inequalities that contain the set of points.

Accepted Answer

A) concave hull 
B) slope 
C) convex hull 
D) geometry

Question 12

The part-worth for each of the attribute levels in a conjoint analysis is determined by

Accepted Answer

A) regression analysis. 
B) sensitivity analysis. 
C) online surveys. 
D) word-of-mouth.

Question 13

Which of the following is a likely constraint on the production quantity x associated with a maximum value and a setup variable y in a fixed-cost problem?

Accepted Answer

A) x ≥ My 
B) x ≤ My 
C) Mx ≤ y 
D) xy ≥ M

Question 14

In order to choose the best solution for implementation, practitioners usually recommend re-solving the integer linear program several times with variations in the

Accepted Answer

A) objective function. 
B) decision variables. 
C) constraint coefficients. 
D) integer constraints.

Question 15

Coming up with a product design that will have the highest utility for a sufficient number of people to ensure sufficient sales to justify making the product is known as the ___________ problem in marketing literature.

Accepted Answer

A) capital budgeting 
B) share of choice 
C) fixed-cost 
D) traveling-salesman

Question 16

An apparel designing company is planning to enter the women's trousers market. They are in the process of developing a product that will appeal most to customers. What category does the above objective fall under?

Accepted Answer

A) Capital budgeting problem 
B) Covering problem 
C) Fixed-cost problem 
D) Product design and market share optimization problem

Question 17

Which of the following is true about the sensitivity analysis for integer optimization problems?

Accepted Answer

A) Sensitivity reports are readily available for integer optimization problems similar to the linear programming problems. 
B) Because of the discrete nature of the integer optimization, Excel Solver takes much more time to calculate objective function coefficient ranges, shadow prices, and right-hand-side ranges. 
C) The sensitivity analysis is not important for integer problems. 
D) To determine the sensitivity of the solution to changes in model inputs for integer optimization problems, the data must be changed and the problem must be re-solved.

Question 18

Based upon the optimal solution and slack variables, what recommendations could you make to management?
​
Where
S = 1 if the store expansion project is accepted; 0 if rejected
F = 1 if the fleet expansion project is accepted; 0 if rejected
M = 1 if the equipment upgrade project is accepted; 0 if rejected
R = 1 if the market research project is accepted; 0 if rejected
and currency is in $1,000s.
Maximize
75S + 50F + 16E + 12R
s.t.
30S + 30F + 10E + 20R ≤ 85
30S + 35F + 20E + 10R ≤ 60
40S + 50F + 20E + 10R ≤ 100
65S + 55F + 20E + 10R ≤ 125
S, F, E, R = 0, 1 (binary)
​

Accepted Answer

The answer of Based upon the optimal solution and slack...

Question 19

What is a binary variable?

Accepted Answer

The answer of What is a binary variable?...

Question 20

In a fixed-cost problem, choosing excessively large values for the maximum production quantity will result in

Accepted Answer

A) all reasonable levels of production. 
B) no production. 
C) no solution at all. 
D) possibly a slow solution procedure.

Exam 13: Integer Linear Optimization Models