Question 1

In cases where Excel Solver experiences excessive run times when solving integer linear problems, the Integer Optimality is set to

Accepted Answer

A) 5%. 
B) 0%. 
C) infinity. 
D) a value equal to the number of integer constraints.

Question 2

A chocolate making company largely produces one particular type of crunchy chocolate bar. Only one of two machines, Machine-1 or Machine-2, can be used to produce this chocolate bar on any given day. The maintenance costs incurred on these two machines per day are $100 and $120, respectively. The manufacturing cost per chocolate bar is $2.5 for Machine-1 and $2 for Machine-2. The maximum daily production capacity for Machine-1 and Machine-2 are 1100 and 1250, respectively. Demand requires that at least 1000 chocolate bars be produced per day. Develop and solve an binary integer programming model for minimizing the total cost.

Accepted Answer

The answer of A chocolate making company largely produces one...

Question 3

FinFone Paper Mill is a small-scale paper-making company which produces four different types of paper. Each type of paper must go through processing on four different machines. The manufacturing time (in minutes) per unit of paper produced is listed in the following table. Time required (in minutes) 
Paper Type
$\begin{array}{ccccc}
\text { Machine Type } & \text { A } & \text { B } & \text { C } & \text { D } \
\hline 1 & 2.4 & 1.2 & 2.7 & 3.2 \
2 & 2.1 & 2.4 & 3.2 & 3.3 \
3 & 1.6 & 0.9 & 2.6 & 5.1 \
4 & 2.5 & 2.5 & 3.2 & 6.5
\end{array}$ ​
The maximum time allotted for each machine is 30 hours per week and at least 100 units of each type of paper should be made during the week.
Profit per unit is: $$\begin{array} { l c c c c } 
\text { Paper Type } & \text { A } & \text { B } & \text { C } & \text { D } \
\hline \text { Profit } ( \$ ) & 0.25 & 0.32 & 0.44 & 0.5
\end{array}$$ ​
Develop and solve an all-integer model that will determine, using the available machine time, the number of units of each paper type to be produced in order to meet the weekly demand and to maximize the profit.

Accepted Answer

The answer of FinFone Paper Mill is a small-scale paper-making...

Question 4

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 5

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 6

A manufacturer makes two types of rubber, Butadiene and Polyisoprene. The plant has two machines, Machine-1 and Machine-2, which are used to make the rubber strips.Manufacturing one strip of Butadiene requires 2.75 hours on Machine-1 and 3 hours on Machine-2. Processing one strip of Polyisoprene, takes 3.5 hours on Machine-1 and 4 hours on Machine-2. Machine-1 is available 180 hours per month, and Machine-2 is available 200 hours per month.Formulate an all-integer mathematical model that will determine how many units of each type of rubber should be produced to maximize profits if the profit contributions of Butadiene and Polyisoprene are $20 and $26, respectively.

Accepted Answer

The answer of A manufacturer makes two types of rubber,...

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

Which of the following approaches to solving integer linear optimization problems tries to identify the convex hull by adding a series of new constraints that do not exclude any feasible integer points?

Accepted Answer

A) Branch-and bound approach 
B) Cutting plane approach 
C) Trial-and-error approach 
D) Convex hull approach

Question 9

__________ is a binary integer programming problem that involves choosing which possible projects or activities provide the best investment return.

Accepted Answer

A) Capital budgeting problem 
B) Fixed-cost problem 
C) Market share optimization problem 
D) Location problem

Question 10

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. The part-worths for each of the attribute levels obtained from an initial customer survey and the subsequent regression analysis can be used to determine the

Accepted Answer

A) customer utility value. 
B) optimal solution for the regression analysis. 
C) overall profit for the company. 
D) overall sales achieved by the company.

Question 11

__________ 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 constraint 
B) Corequisite constraint 
C) k out of n alternatives constraint 
D) Mutually exclusive constraint

Question 12

Which of the following is true about generating alternatives in binary optimization?

Accepted Answer

A) If the second-best solution is very close to optimal, it is always preferred over the true optimal solution because of factors outside the model. 
B) If alternative solutions exist, it would not help management because some factors that make one alternative are not preferred over the factors that make another alternative. 
C) If the solution is a unique optimal solution, it would be good for management to know how much worse the second-best solution is than the unique optimal solution. 
D) If any alternative solution exists, it would only be a second-best next to the optimal solution because there is no third-best or an alternative second-best solution to any binary integer programming problem.

Question 13

The ___________ is the utility value that a consumer attaches to each level of each attribute in a conjoint analysis model.

Accepted Answer

A) weightage 
B) share of choice 
C) part-worth 
D) share of market

Question 14

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 15

A store is offering a discount on 800 pairs of basketball shoes. The amount of the discount varies and is not revealed to the customer until checkout. The distribution of discounts is given in the below table.
​ $$\begin{array} { | l | c | } 
\hline \text { Store Location } & \text { Potential Areas Covered } \
\hline \text { L1 } & 3,4,6,8 \
\hline \text { L2 } & 1,5,9 \
\hline \text { L3 } & 1,4,7 \
\hline \text { L4 } & 2,6,7 \
\hline \text { L5 } & 3,4,9 \
\hline \text { L6 } & 2,7,9 \
\hline \text { L7 } & 4,8,9 \
\hline \text { L8 } & 1,2,5,6 \
\hline \text { L9 } & 3,6,8 \
\hline
\end{array}$$ ​
Formulate an integer programming model that could be used to find the minimum number of stores to open in order to cover customers of all areas for the home delivery service.

Accepted Answer

The answer of A store is offering a discount on...

Question 16

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.

Exam 12: Integer Linear Optimization Models