Question 1

Consider the following linear programming problem:
 $$\begin{array} { l } 
\text { Max: } 500 A + 700 B \
\text { Subject to: } \
2 A + 3 B \leq 35 \text { (assembly hours) } \
3 A + 5 B \leq 40 \text { (machine hours) }
\end{array}$$ 
Reformulate and solve this problem as a goal programming problem if the following goals,with their associated weights,must be met.
Goal 1: Produce at least 15 units of product A;Weight 15
Goal 2: Produce at least 15 units of product B;Weight 15
Goal 3: Minimize overtime in assembly department;Weight 25
Goal 4: Minimize overtime in machine department;Weight 25
Goal 5: Achieve at least $100,000 in profit;Weight 20

Accepted Answer

The answer of Consider the following linear programming problem:
 \[\begin{array}...

Question 2

A company is considering producing 8 different products for the upcoming holiday season.The profit contribution per product is illustrated below:
 $$\begin{array} { l l } 
\text { Product } & \text { Profit } ( \$ ) \
\hline 1 & 10 \
2 & 12 \
3 & 7 \
4 & 15 \
5 & 8 \
6 & 9 \
7 & 13 \
8 & 11
\end{array}$$ 
The marketing manager has imposed the following restrictions on the production mix:
•Since products 1,2,and 3 are electronic gadgets,at least two of these products must be in the production mix.
•Since products 4 and 5 are kids-oriented,the production mix must include no more than one of these products.
•If product 7 is included in the mix,then product 8 must be included,and vice versa.
Which products should be included in the mix to maximize profit?

Accepted Answer

The answer of A company is considering producing 8 different...

Question 3

A company produces four products each of which must undergo assembly,inspection,and packaging.The information below summarizes the hours required for each operation by each product,the total hourly capacity for each operation,and the fixed cost incurred by each product if it is produced.
  
Each unit of product 1 sold will contribute $60 to profit,and each unit of products 2,3,and 4 contributes $65,$70,and $55,respectively.What is the optimal product mix?

Accepted Answer

The answer of A company produces four products each of...

Question 4

The deviational variable di‾ indicates the amount by which a certain goal is:

Accepted Answer

A) overachieved 
B) over attained 
C) binding 
D) underachieved 
E) non-binding

Question 5

Set up and solve the following nonlinear programming problem using Excel:
 $$\begin{array} { l } 
\text { Max: } \mathrm { X } _ { 1 } + 2 \mathrm { X } _ { 2 } + 3 \mathrm { X } _ { 1 } \mathrm { X } _ { 2 } + 5 \mathrm { X } _ { 3 } 3 \
\text { Subject to } \
\mathrm { X } _ { 1 } + \mathrm { X } _ { 2 } + \mathrm { X } _ { 3 } \leq 75 \
\mathrm { X } _ { 1 } + \mathrm { X } _ { 2 } \geq 15 \
2 \mathrm { X } _ { 1 } + 2 \mathrm { X } _ { 3 } \leq 40 \
\mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } , \mathrm { X } _ { 3 } \geq 0
\end{array}$$

Accepted Answer

The answer of Set up and solve the following nonlinear...

Question 6

There is no precise way to know where to start the solution search process for an NLP model.

Accepted Answer

A) True 
 B)False

Question 7

An integer programming problem assumes that its objective function and its constraints are linear.

Accepted Answer

A) True 
 B)False

Question 8

Deviational variables assume the value zero if a goal is completely attained.

Accepted Answer

A) True 
 B)False

Question 9

Rounding off the solution to an LP relaxation problem may sometimes yield an infeasible solution to an IP problem.

Accepted Answer

A) True 
 B)False

Question 10

An investment strategy restricts the portfolio to a mix of two stocks A and B with the following price/share and annual returns:
$\begin{array}{ccc}
\text { Stock } & \text { Price/Share } & \text { Annual Return } \
 \mathrm{A} & \$ 35 & 5 \% \
\mathrm{~B} & \$ 45 & 7 \%
\end{array}$

Assume that the maximum amount available for investment is $100,000 with the following 2 prioritized investment goals:
Rank R1: Obtain an annual return of at least 6%.
Rank R2: Limit the investment in stock B to no more than 55% of the total investment.
Assume X? = dollar amount allocated to stock A,and X? = dollar amount allocated to stock B.
What is the objective function?

Accepted Answer

A) Min d?? + d?? 
B) Min R?(d??)+ R?(d??) 
C) Min R?(d??)- R?(d??) 
D) Min R?(d??)+ R?(d??) 
E) Min R?(d??)+ R?(d??)

Question 11

A company wants to select one product from a set of 3 possible products.Which of the following ensures that only one product will be selected?

Accepted Answer

A) XA + XB + XC = 1 
B) XA + XB + XC ≤ 1 
C) XA + XB + XC ≥ 1 
D) XA + XB + XC ≥ 0 
E) XA - XB - XC = 1

Question 12

An investor is considering 7 different stocks: A,B,C,D,E,F,and G.The expected annual return for each stock is provided as follows:
 $$\begin{array}{l}
\quad \quad \quad \quad \text { Annual }\
\begin{array} { l l } 
\text { Stock } & \text { Return } \
\text { A } & 9.5 \% \
\mathrm {~B} & 8.0 \% \
\mathrm { C } & 7.0 \% \
\mathrm { D } & 10.0 \% \
\mathrm { E } & 8.0 \% \
\mathrm {~F} & 9.0 \% \
\mathrm { G } & 10 \%
\end{array}
\end{array}$$ 
The investor has imposed the following restrictions regarding the composition of the portfolio:
•the portfolio must include exactly one of the following stocks: either A or B.
•if stock B is selected,then stock F must also be selected.
•if stock D is selected,then stock E must be excluded.
Which stocks should be included in the portfolio to maximize annual return?

Accepted Answer

The answer of An investor is considering 7 different stocks:...

Question 13

Consider the following profit expected from each dollar (Xᵢ)spent in the following advertising media:
  
How should the advertising budget be allocated if the company wants to spend at least $1000 on each medium without exceeding its $10,000 budget?

Accepted Answer

The answer of Consider the following profit expected from each...

Question 14

A marketing manager is considering the following advertising media to promote a new
product.
  
The marketing manager has established the following goals,stated in no particular order,for the advertising campaign:
Goal 1: Reach at least 500,000 individuals.
Goal 2: Limit the total spending to $150,000.
Formulate and solve this goal programming problem.

Accepted Answer

The answer of A marketing manager is considering the following...

Question 15

A company wants to select 2 products from a set of four possible products.Which of the following constraints ensures that no more than 3 will be selected?

Accepted Answer

A) XA + XB + XC + XD = 3 
B) XA + XB + XC + XD ≥ 0 
C) XA + XB + XC + XD ≤ 3 
D) XA + XB + XC + XD ≥ 3 
E) XA + XB + XC + XD ≠ 3

Exam 6: Integer, Goal, and Nonlinear Programming Models

The deviational variable di‾ indicates the amount by which a certain goal is:

There is no precise way to know where to start the solution search process for an NLP model.

An integer programming problem assumes that its objective function and its constraints are linear.

Deviational variables assume the value zero if a goal is completely attained.

Rounding off the solution to an LP relaxation problem may sometimes yield an infeasible solution to an IP problem.

A company wants to select one product from a set of 3 possible products.Which of the following ensures that only one product will be selected?

Consider the following profit expected from each dollar (Xᵢ)spent in the following advertising media: How should the advertising budget be allocated if the company wants to spend at least $1000 on each medium without exceeding its $10,000 budget?

A company wants to select 2 products from a set of four possible products.Which of the following constraints ensures that no more than 3 will be selected?