Question 1

Which tab in the Risk Solver Platform (RSP) task pane is used to define an optimization problem?

Accepted Answer

A)  Guess 
B)  Model 
C)  Change 
D)  Delete 
A)  Guess 
B)  Model 
C)  Change 
D)  Delete

Question 2

A hospital needs to determine how many nurses to hire to cover a 24 hour period. The nurses must work 8 consecutive hours but can start work at the start of 6 different shifts. They are paid different wages depending on when they start their shifts. The number of nurses required per 4-hour time period and their wages are shown in the following table.
 $\begin{array}{lcc}
\text { Time period } & \text { Required \# of Nurses } & \text { Wage }(\$ / \mathrm{hr}) \
\hline 12 \mathrm{am}-4 \mathrm{am} & 20 & 15 \
4 \mathrm{am}-8 & 30 & 16 \
\text { am } & & \
8 \mathrm{am}-12 \mathrm{pm} & 40 & 13 \
12 \mathrm{pm}-4 \mathrm{pm} & 50 & 13 \
4 \mathrm{pm}-48 & 40 & 14 \
\mathrm{pm} \
8 \mathrm{pm}-12 \mathrm{am}&30 & 15 
\end{array}$
 Enter the numbers in the appropriate cells of ranges B6:G11 and B13:G13 in the Excel spreadsheet to solve this problem based on the following formulation.
 Let $\quad X _ { i } =$ mumber of nurses warking in thme period $i ; i = 1,6$
$$\begin{array} { l l } 
\text { MiN: } & 1 \mathbf { X } _ { 1 } + 1 \mathbf { X } _ { \mathbf { 2 } } + 1 \mathbf { X } _ { \mathbf { 3 } } + 1 \mathbf { X } _ { 4 } + 1 \mathbf { X } _ { \mathbf { 5 } } + 1 \mathbf { X } _ { \mathbf { 6 } } \
\text { Subject ta: } & 1 \mathbf { X } _ { 1 } + 1 \mathbf { X } _ { \mathbf { z } } \geq 30 \
& 1 \mathbf { X } _ { \mathbf { 2 } } + 1 \mathbf { X } _ { \mathbf { 3 } } \geq 40 \
& 1 \mathbf { X } _ { \mathbf { 3 } } + 1 \mathbf { X } _ { 4 } \geq 50 \
& 1 \mathbf { X } _ { 4 } + 1 \mathbf { X } _ { \mathbf { 5 } } \geq 40 \
& 1 \mathbf { X } _ { 5 } + 1 \mathbf { X } _ { \mathbf { 1 } } \geq 30 \
& 1 \mathbf { X } _ { 1 } + 1 \mathbf { X } _ { \mathbf { 1 } } \geq 20 \
& \mathbf { X } _ { \mathrm { i } } \geq 0
\end{array}$$

Accepted Answer

The answer of A hospital needs to determine how many...

Question 3

You have been given the following linear programming model and Excel spreadsheet to solve this problem. What cell references would you enter in the Risk Solver Platform (RSP) task pane for the following?
Objective Cell:
Variables Cells:
Constraints Cells:
 $$\begin{array} { l l } 
\text { MAX: } & 8 X _ { 1 } + 5 X _ { 2 } \
\text { Subject to: } & 3 X _ { 1 } + 5 X _ { 2 } = 54 \
& 11 X _ { 1 } + 10 X _ { 2 } \leq 144 \
& X _ { 1 } \geq 12 \
& X _ { 1 } X _ { 2 } \geq 0
\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } 
\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \
\hline 1 & & & & & \
\hline 2 & & & & & \
\hline 3 & & \mathrm { X } _ { 1 } & \mathrm { X } _ { 2 } & & \
\hline 4 & \text { Number to make: } & & & & \text { OBJ. FN. VALUE } \
\hline 5 & \text { Unit profit: } & 8 & 5 & & \
\hline 6 & & & & & \
\hline 7 & \text { Constraints: } & & & \text { Used } & \text { Available } \
\hline 8 & 1 & 3 & 5 & & 54 \
\hline 9 & 2 & 11 & 10 & & 144 \
\hline 10 & 3 & 1 & 0 & & 12 \
\hline
\end{array}$$

Accepted Answer

The answer of You have been given the following linear...

Question 4

A company is planning production for the next 4 quarters. They want to minimize the cost of production. The production cost, demand and production capacity vary from quarter to quarter. The maximum amount of inventory which can be held is 100 units and management wants to keep at least 50 units on hand. Quarterly inventory holding cost is 4% of the cost of production. There are currently 50 units in inventory. The company wants to produce at no less than one half of its maximum capacity in any quarter.
 $$\begin{array}{l}
\text {\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad Quarter }\
\begin{array} { l c c c c } 
 & 1 & 2 & 3 & 4 \
\hline \text { Unit Production Cost } & \$ 55 & \$ 50 & \$ 50 & \$ 45 \
\text { Units Demanded } & 100 & 150 & 180 & 120 \
\text { Maramum Praduction } & 150 & 150 & 160 & 130 \
\text { Holding cost } & \$ 2.2 & \$ 2 & \$ 2 & \$ 1.8
\end{array}
\end{array}$$ $\begin{array} { l } 
\text { Let } \quad P _ { i } = \text { number of units produced in quarter } i , i = 1 , \ldots , 4 \
\mathbf { B } _ { i } = \text { beginning inventory far quarter } i \
\end{array}$

$\begin{array}{ll}
\text { MIN: } & 55 \mathrm{P}_{1}+50 \mathrm{P}_{2}+50 \mathrm{P}_{3}+45 \mathrm{P}_{4}+ \
& 2.2\left(\mathrm{~B}_{1}+\mathrm{B}_{2}\right) / 2+2\left(\mathrm{~B}_{2}+\mathrm{B}_{3}\right) / 2+2\left(\mathrm{~B}_{3}+\mathrm{B}_{4}\right) / 2+1.8\left(\mathrm{~B}_{4}+\mathrm{B}_{5}\right) / 2 \
\text { Subject to: } & 75 \leq \mathrm{P}_{1} \leq 150 \
&75 \leq \mathrm{P}_{2} \leq 150 \
& 80 \leq \mathrm{P}_{3} \leq 160 \
& 65 \leq \mathrm{P}_{4} \leq 130 \
& 50 \leq \mathrm{B}_{1}+\mathrm{P}_{1}-100 \leq 100 \
& 50 \leq \mathrm{B}_{2}+\mathrm{P}_{2}-150 \leq 100 \
& 50 \leq \mathrm{B}_{3}+\mathrm{P}_{3}-180 \leq 100 \
& 50 \leq \mathrm{B}_{4}+\mathrm{P}_{4}-120 \leq 100 \
&\mathrm{~B}_{2}=\mathrm{B}_{1}+\mathrm{P}_{1}-100 \
& \mathrm{~B}_{3}=\mathrm{B}_{2}+\mathrm{P}_{2}-150 \
&\mathrm{~B}_{4}=\mathrm{B}_{3}+\mathrm{P}_{3}-180 \
& \mathrm{~B}_{5}=\mathrm{B}_{4}+\mathrm{P}_{4}-120 \
& \mathrm{P}_{\mathrm{i}} \mathrm{B}_{\mathrm{i}} \geq 0
\end{array}$   What formulas are required for cells D3, D6, D8, D15, D17 and D18 in the Excel spreadsheet implementation of the formulation?

Accepted Answer

The answer of A company is planning production for the...

Question 5

Which type of spreadsheet cell represents the decision variables in an LP model?

Accepted Answer

A)  Target or set cell 
B)  Variable cell 
C)  Constraint cell 
D)  Constant cell 
A)  Target or set cell 
B)  Variable cell 
C)  Constraint cell 
D)  Constant cell

Question 6

The hospital administrators at New Hope, County General, and City East recently received notice of an impending state inspection of their facilities. Under new guidelines established to improve the overall health care system, state inspectors will be assessing the efficiency of each hospital. The staff at New Hope has suggested a mutual assistance program in preparation for the inspections and have proposed using DEA as a means to assess the efficiency of each facility. The data collected thus far is summarized in the following table. All data reflects averages compiled over the past six months.
 $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\text { Hospital }$
$\begin{array}{lccc}
&\text { New Hope } & \text { Countv General } & \text { City East }\
\hline \text { Input Measures } & & & \
\text { Bed days unused (1000s) } & 83.0 & 105.0 & 104.1 \
\text { Supply expense }(\$ 1000 \mathrm{~s}) & 123.8 & 162.3 & 154.0 \
\text { Full-time staff } & 225.0 & 200.0 & 231.0 \
\text { Output Measures } & & & \
\text { Patient-days (1000s) } & 105.0 & 71.0 & 82.7 \
\text { Nurses qualified } & 253.0 & 92.0 & 175.0 \
\text { Assistants on staff } & 125.0 & 45.0 & 65.0 \
\text { satiefartion } & 98.0 & 88.0 & 83.0
\end{array}$

What are the key formulas for this Excel spreadsheet implementation of the following formulation?
 Let $\quad w _ { i } =$ werght as5igned to dutput $j , j = 1 , \ldots , 4$
$\mathbf { v } _ { i } =$ waight as5igned to ingut $i , i = 1 , \ldots , 3$
MAX: $0 0. \quad 82.7 w _ { 1 } + 175 .0 w _ {2 } + 65.0 w _ { 3 } + 83 .0 w _ { 4 }$
Subject ta:
$105.1 w _ { 1 } + 253.0 w _ { 2} + 125.0 w _ { 3 } + 98.0 w _ { 4 } - 83.0 v _ { 1 } - 123.8 v _ { 2 } - 225.0 v _ { 3 } \leq 0$
$71.0 w _ { 1 } + 92.0 w _ { 2 } + 45.0 w _ { 3 } + 88.0 w _ { 4 } - 105.0 v _ { 1 } - 162.3 v _ { 2 } - 200 v _ { 3 } \leq 0$
$82.7 w _ { 1 } + 175.0 w _ { 2} + 65.0 w _ { 3 } + 83.0 w _ { 4 } - 104.1 v _ { 1 } - 154.0 v _ { 2 } - 231.0 v _ { 3 } \leq0$
$104.1 \mathbf { v } _ { 1 } + 154.0 \mathbf { v } _ { \mathbf { 2 } } + 231.0 \mathbf { v } _ { \mathbf { 3 } } = 1$
$w _ { 1 , } w _ { 2 } w _ { 3 , } w _ { 4 } , \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } \geq0$

Accepted Answer

The answer of The hospital administrators at New Hope, County...

Question 7

Exhibit 3.1
The following questions are based on this problem and accompanying Excel windows.
Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.
 Let
$$\begin{array} { l } 
\mathrm { X } _ { 1 } = \text { Number of Beds to produce } \
\mathrm { X } _ { 2 } = \text { Number of Desks to produce }
\end{array}$$ The LP model for the problem is
 $$\begin{array} { l l } 
\text { MAX: } & 30 X _ { 1 } + 40 X _ { 2 } \
\text { Subject to: } & 6 X _ { 1 } + 4 X _ { 2 } \leq 36 \text { (carpentry) } \
& 4 X _ { 1 } + 8 X _ { 2 } \leq 40 \text { (varnishing) } \
& X _ { 2 } \leq 8 \text { (demand for desks) } \
& X _ { 1 } , X _ { 2 } \geq 0
\end{array}$$  
-Refer to Exhibit 3.1. Which of the following statements represent the carpentry, varnishing and limited demand for desks constraints?

Accepted Answer

A)  B4:C4$\le$B5:C5 
B)  E5$\le$ 0 
C)  D8:D10 $\le$E8:E10 
D)  E8:E10$\le$D8:D10 
A)  B4:C4$\le$B5:C5 
B)  E5$\le$ 0 
C)  D8:D10 $\le$E8:E10 
D)  E8:E10$\le$D8:D10

Question 8

A farmer is planning his spring planting. He has 20 acres on which he can plant a combination of Corn, Pumpkins and Beans. He wants to maximize his profit but there is a limited demand for each crop. Each crop also requires fertilizer and irrigation water which are in short supply. There are only 50 acre ft of irrigation available and only 8,000 pounds/acre of fertilizer available. The following table summarizes the data for the problem.
 $$\begin{array} { l | c c c c c } 
\text { Crop } & \begin{array} { c } 
\text { Profit per } \
\text { Acre } ( \$ )
\end{array} & \begin{array} { c } 
\text { Yield per } \
\text { Acre (Ib) }
\end{array} & \begin{array} { c } 
\text { Maximum } \
\text { Demand (Ib) }
\end{array} & \begin{array} { c } 
\text { Irrigation } \
\text { (acre ft) }
\end{array} & \begin{array} { c } 
\text { Fertilizer } \
\text { (pounds/acre) }
\end{array} \
\hline \text { Corn } & 2,100 & 21,000 & 200,000 & 2 & 500 \
\text { Pumpkin } & 900 & 10,000 & 180,000 & 3 & 400 \
\text { Beans } & 1,050 & 3,500 & 80,000 & 1 & 300
\end{array}$$ Enter the numbers in the appropriate cells of ranges B12:D12 and E8:F12 in the Excel spreadsheet to solve this problem based on the following formulation.
 Let
$\begin{array} { l } 
X _ { 1 } = \text { aces of corn } \
X _ { 2 } = \text { acres of pumpkin } \
X _ { 3 } = \text { acres of beans }
\end{array}$

MAX: $\quad 2100 \mathrm { X } _ { 1 } + 900 \mathrm { X } _ { 2 } + 1050 \mathrm { X } _ { 3 }$
Subject to: $\quad 21 X _ { 1 } \leq 200$
$10 \mathrm { X } _ { 2 } \leq 180$
$3.5 \mathrm { X } _ { 3 } \leq 80$
$\mathrm { X } _ { 1 } + \mathrm { X } _ { 2 } + \mathrm { X } _ { 3 } \leq 20$
$2 \mathrm { X } _ { 1 } + 3 \mathrm { X } _ { 2 } + 1 \mathrm { X } _ { 3 } \leq 50$
$5 \mathrm { X } _ { 1 } + 4 \mathrm { X } _ { 2 } + 3 \mathrm { X } _ { 3 } \leq 80$
$\mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } , \mathrm { X } _ { 3 } \geq 0$ $$\begin{array} { | c | l | c | c | c | c | c | } 
\hline & { \text { A } } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \
\hline 1 & & \text { Farm } & \text { Planning } & \text { Problem } & & \
\hline 2 & & & & & & \
\hline 3 & & \text { Corn } & \text { Pumpkin } & \text { Beans } & & \
\hline 4 & \text { Acres to plant } & & & & & \text { Total Profit: } \
\hline 5 & \text { Profit per acre } & & & & & \
\hline 6 & & & & & & \
\hline 7 & \text { Constraints: } & & & & \text { Used } & \text { Available } \
\hline 8 & \text { Corn demand } & & & & & \
\hline 9 & \text { Pumpkin demand } & & & & & \
\hline 10 & \text { Bean demand } & & & & & \
\hline 11 & \text { Water } & & & & & \
\hline 12 & \text { Fertilizer } & & & & & \
\hline
\end{array}$$

Accepted Answer

The answer of A farmer is planning his spring planting....

Question 9

You have been given the following linear programming model and Excel spreadsheet to solve this problem. What cell references would you enter in the Risk Solver Platform (RSP) task pane for the following?
Objective Cell:
Variables Cells:
Constraints Cells:
 MIN: $\quad 8 X _ { 1 } + 3 X _ { 2 }$
Subject to: $\quad X _ { 2 } \geq 8$
$\begin{array} { l } 
8 \mathrm { X } _ { 1 } + 5 \mathrm { X } _ { 2 } \geq 80 \
3 \mathrm { X } _ { 1 } + 5 \mathrm { X } _ { 2 } \geq 60 \
\mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } \geq 0
\end{array}$ $$\begin{array} { | c | c | c | c | c | c | } 
\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \
\hline 1 & & & & & \
\hline 2 & & & & & \
\hline 3 & & \mathrm { X } _ { 1 } & \mathrm { X } _ { 2 } & & \
\hline 4 & \text { Number to make: } & & & & \text { OBJ. FN. VALUE } \
\hline 5 & \text { Unit profit: } & & & & \
\hline 6 & & & & & \
\hline 7 & \text { Constraints: } & & & \text { Used } & \text { Available } \
\hline 8 & 1 & & 1 & & 8 \
\hline 9 & 2 & 8 & 5 & & 80 \
\hline 10 & 3 & 3 & 5 & & 60 \
\hline
\end{array}$$

Accepted Answer

The answer of You have been given the following linear...

Question 10

Carlton construction is supplying building materials for a new mall construction project in Kansas. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Carlton's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking, at least 40% of the total delivered be delivered by railway, and up to 15% of the total delivered be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons):
 $\begin{array}{cccc}
\text { Week } & \text { Trucking Limts } & \text { Ralway Limits } & \text { Air Cargo Limits } \
\hline 1 & 45 & 60 & 15 \
2 & 50 & 55 & 10 \
3 & 55 & 45 & 5 \
\hline \text { Costs }(\$ \text { per } 1000 \text { tons }) & \$ 200 & \$ 140 & \$ 400
\end{array}$
 Formulate an LP model for this logistics problem.

Accepted Answer

The answer of Carlton construction is supplying building materials for...

Question 11

Robert Hope received a welcome surprise in this management science class; the instructor has decided to let each person define the percentage contribution to their grade for each of the graded instruments used in the class. These instruments were: homework, an individual project, a mid-term exam, and a final exam. Robert's grades on these instruments were 75, 94, 85, and 92, respectively. However, the instructor complicated Robert's task somewhat by adding the following stipulations:
 -homewark can account far up to $25 \%$ of the grade, but must be at least $5 \%$ af the grade;
- the praject can account for up to $25 \%$ of the grade, but must be at least $5 \%$ af the grade;
- the mid-term and final must each accaunt far betwen $10 \%$ and $40 \%$ of the grade but cannot accaunt far mare than $7 \%$ of the grade when the percentages are cambined; and
- the project and final exam grades may not collectively constitute more than $50 \%$ of the Iratade. The following LP model allows Robert to maximize his numerical grade.
 $\begin{array} { l } 
\text { Let } \quad W _ { 1 } = \text { weight assigned to hamewark } \
 \quad \quad  \quad W _ { \mathbf { 2 } } = \text { waight assigned to the praject } \
\quad \quad \quad W _ { 3 } = \text { weight assigned to the midi-term } \
 \quad \quad \quad W _ { 4 } = \text { waight assigned to the final } \
\
\text { MAX: } \quad 75 \mathrm {~W} _ { 1 } + 94 \mathrm {~W} _ { 2 } + 85 \mathrm {~W} _ { 3 } + 92 \mathrm {~W} _ { 4 } \
\text { Subject to: } \quad W _ { 1 } + W _ { 2 } + W _ { 3 } + W _ { 4 } = 1 \
 \quad \quad \quad \quad \quad  \quad W _ { 3 } + W _ { 4 } \leq0 .70 \
 \quad \quad \quad \quad \quad \quad W _ { 3 } + W _ { 4 } \geq 0.50 \
 \quad \quad \quad \quad \quad \quad\text { 0. } 05 \leq W _ { 1 } \leq 0.25 \
 \quad \quad \quad \quad \quad \quad\text { 0. } 05 \leq W _ { 2 } \leq 0.25 \
 \quad \quad \quad \quad \quad \quad\text { 0.10 } \leq W _ { 3 } \leq 0 .4 0 \
 \quad \quad \quad \quad \quad \quad0 .10 \leq W _ { 4 } \leq 0.40 \
\end{array}$    What values would you enter in the Risk Solver Platform (RSP) task pane for the cells in this Excel spreadsheet implementation of this problem?
Objective Cell:
Variables Cells:
Constraints Cells:

Accepted Answer

The answer of Robert Hope received a welcome surprise in...

Question 12

You have been given the following linear programming model and Excel spreadsheet to solve this problem. What cell references would you enter in the Risk Solver Platform (RSP) task pane for the following?
Objective Cell:
Variables Cells:
Constraints Cells:
 $$\begin{array} { l l } 
\text { MAX: } & 12 X _ { 1 } + 9 X _ { 2 } \
\text { Subject to: } & 9 X _ { 1 } + 10.5 X _ { 2 } \leq 126 \
& X _ { 1 } \geq 5 \
& X _ { 2 } \geq 6 \
& X _ { 1 } , X _ { 2 } \geq 0
\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } 
\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \
\hline 1 & & & & & \
\hline 2 & & & & & \
\hline 3 & & \mathrm { X } _ { 1 } & \mathrm { X } _ { 2 } & & \
\hline 4 & \text { Number to make: } & & & & \text { OBJ. FN. VALUE } \
\hline 5 & \text { Unit profit: } & 12 & 9 & & \
\hline 6 & & & & & \
\hline 7 & \text { Constraints: } & & & \text { Used } & \text { Available } \
\hline 8 & 1 & 9 & 10.5 & & 126 \
\hline 9 & 2 & 1 & 0 & & 5 \
\hline 10 & 3 & 0 & 1 & & 6 \
\hline
\end{array}$$

Accepted Answer

The answer of You have been given the following linear...

Question 13

Project 3.1- The Diet Problem: Ordering Meals from McDonald's
Based on: Robert A. Bosch, "Big Mac Attack: The Diet Problem revisited, Eating at McDonald's," OR/MS Today, August 1993, pp 30-31.
Tina Simpson is a new fourth-grade teacher at Forest Ridge Elementary. The first teacher workshop for the upcoming school year is next Monday and by majority vote, McDonald's was selected as the food of choice. As the new person, Tina is tasked with developing the meal for the workshop. McDonald's has graciously offered to deliver whatever food Tina decides to order, along with a variety of condiments applicable to whatever is ordered. Rather than offer a menu choice, Tina has decided to simply order the same meal for each person in the workshop.
To get started, Tina took a trip to McDonald's and obtained their published information on the nutritional content of their food. That data is summarized in the table below.
     Tina wants the meal to be nutritionally complete. The National Research Council publishes their Recommended Daily Allowances. In this publication, they contend that a diet (in this case the meal) should provide at least 100 percent of the U.S. RDA of numerous nutrients. The specific amount of the RDA depends on such factors as age, weight and gender. In addition, the council recommends daily sodium and cholesterol intakes be kept to at most 2.4 grams of sodium and 300 milligrams of cholesterol. Further, at most 30 percent of the calories consumed should come from fat, and at most 10 percent from saturated fat. Each gram of fat contains 9 calories.
Based on the above information, Tina wants to design a least-cost meal that provides at least 100% of the U.S. RDA of vitamins A, C, B1, B2, niacin, calcium, and iron; supplies at least 55 grams of protein; contains at most 3 grams of sodium; and contains at most 30 percent of its calories from fat. Only those foods list in the table above are available for the meal.
Formulate the LP model for Tina's problem. Develop a spreadsheet model of the problem and use Excel Solver to determine the least-cost meal that meets all the stated requirements.
What is the recommended meal? Is this meal reasonable? If not, modify the model to obtain what you believe to be a reasonable meal that meets the stated requirements.

Accepted Answer

Question 14

The English-reading eye scans

Accepted Answer

A)  Right to left 
B)  Bottom to top 
C)  Left to Bottom 
D)  Left to right 
A)  Right to left 
B)  Bottom to top 
C)  Left to Bottom 
D)  Left to right

Question 15

Which of the following describes Data Envelopment Analysis (DEA).

Accepted Answer

A)  DEA finds the most effective company among some set of companies. 
B)  DEA determines if a company is converting inputs to outputs as effectively as possible. 
C)  DEA determines how effective a company converts inputs to outputs compared to other companies. 
D)  DEA compares how effective a company converts inputs to outputs compared to a benchmark composite of all companies. 
A)  DEA finds the most effective company among some set of companies. 
B)  DEA determines if a company is converting inputs to outputs as effectively as possible. 
C)  DEA determines how effective a company converts inputs to outputs compared to other companies. 
D)  DEA compares how effective a company converts inputs to outputs compared to a benchmark composite of all companies.

Question 16

A financial planner wants to design a portfolio of investments for a client. The client has $400,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 30% of the money in any one investment, at least one half should be invested in long-term bonds which mature in six or more years, and no more than 40% of the total money should be invested in B or C since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio.
 $$\begin{array} { c c c l } 
\text { Investment } & \text { Return } & \text { Years to Maturity } & \text { Rating } \
\hline \mathbf { A } & 6.45 \% & 6 & \text { 1-Excellent } \
\text { B } & 8.5 \% & 5 & \text { 3-Gaod } \
\text { C } & 9.00 \% & 8 & \text { 4-Fair } \
\text { D } & 7.75 \% & 4 & \text { 2-Very Gaod }
\end{array}$$ \[\begin{array} { l l } 
\text { Let } & \mathbf { X } _ { 1 } = \text { Dollars invested in } \mathrm { A } \
& \mathbf { X } _ { \mathbf { 2 } } = \text { Dollars invested in } \mathrm { B } \
& \mathbf { X } _ { \mathbf { 3 } } = \text { Dollars invested in } \mathrm { C } \
& \mathbf { X } _ { 4 } = \text { Dollars invested in } \mathrm { D } \
& \ 
\text { MAX: }  & \mathbf { X } 45 \mathbf { X } _ { 1 } + .085 \mathbf { X } _ { \mathbf { 2 } } + \text {. } 990 \mathbf { X } _ { \mathbf { 3 } } + .075 \mathbf { X } _ { 4 } \
\text { Subject to: } & \mathbf { X } _ { 1 } + \mathbf { X } _ { \mathbf { 2 } } + \mathbf { X } _ { \mathbf { 3 } } + \mathbf { X } _ { 4 } \leq 400000 \
& \mathbf { X } _ { 1 } \leq 120000 \
& \mathbf { X } _ { \mathbf { 2 } } \leq 120000 \
& \mathbf { X } _ { 3 } \leq 120000 \
& \mathbf { X } _ { 4 } \leq 120000 \
& \mathbf { X } _ { 1 } + \mathbf { X } _ { 3 } \geq 200000 \
& \mathbf { X } _ { \mathbf { 2 } } + \mathbf { X } _ { 3 } \leq 160000 \
& \mathbf { X } _ { 1 } \mathbf { X } _ { \mathbf { 2 } } \mathbf { X } _ { \mathbf { 3 } } \mathbf { X } _ { 4 } \geq 0
\end{array}\]     What formulas are required for the following cells in the Excel spreadsheet implementation of the formulation?
B7
D7
F7
H7

Accepted Answer

The answer of A financial planner wants to design a...

Question 17

Spreadsheet modeling is an acquired skill because

Accepted Answer

A)  there is generally only one correct way to build a model. 
B)  the spreadsheet is free-form providing many modeling options. 
C)  using Risk Solver Platform (RSP) requires lots of experience. 
D)  spreadsheets are not very easy to use. 
A)  there is generally only one correct way to build a model. 
B)  the spreadsheet is free-form providing many modeling options. 
C)  using Risk Solver Platform (RSP) requires lots of experience. 
D)  spreadsheets are not very easy to use.

Question 18

The "Objective Value of" option in the Risk Solver Platform (RSP) task pane may be used to

Accepted Answer

A)  find a solution at a maximum value. 
B)  find a solution at a minimum value. 
C)  find a solution for a specific objective function value. 
D)  returns the best feasible solution. 
A)  find a solution at a maximum value. 
B)  find a solution at a minimum value. 
C)  find a solution for a specific objective function value. 
D)  returns the best feasible solution.

Question 19

You have been given the following linear programming model and Excel spreadsheet to solve this problem. What numbers should be entered into cells B5:C5 and B8:C10 to implement this model?
 $$\begin{array} { l l } 
\text { MAX: } & 4 X _ { 1 } + 3 X _ { 2 } \
\text { Subject to: } & 6 X _ { 1 } + 7 X _ { 2 } \leq 84 \
& X _ { 1 } \leq 10 \
& X _ { 2 } \leq 8 \
& X _ { 1 } , X _ { 2 } \geq 0
\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } 
\hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \
\hline 1 & & & & & \
\hline 2 & & & & & \
\hline 3 & & X _ { 1 } & \mathrm { X } _ { 2 } & & \
\hline 4 & \text { Number to make: } & & & & \text { OBJ. FN. VALUE } \
\hline 5 & \text { Unit profit: } & & & & \
\hline 6 & & & & & \
\hline 7 & \text { Constraints: } & & & \text { Used } & \text { Available } \
\hline 8 & 1 & & & & 84 \
\hline 9 & 2 & & & & 10 \
\hline 10 & 3 & & & & 8 \
\hline
\end{array}$$

Accepted Answer

The answer of You have been given the following linear...

Question 20

A financial planner wants to design a portfolio of investments for a client. The client has $400,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 30% of the money in any one investment, at least one half should be invested in long-term bonds which mature in six or more years, and no more than 40% of the total money should be invested in B or C since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio.
 $$\begin{array} { c c c l } 
\text { Investment } & \text { Return } & \text { Years to Maturity } & \text { Rating } \
\hline \mathbf { A } & 6.45 \% & 6 & \text { 1-Excellent } \
\text { B } & 8.5 \% & 5 & \text { 3-Gaod } \
\text { C } & 9.00 \% & 8 & \text { 4-Fair } \
\text { D } & 7.75 \% & 4 & \text { 2-Very Gaod }
\end{array}$$ Formulate the LP for this problem.

Accepted Answer

The answer of A financial planner wants to design a...

Which tab in the Risk Solver Platform (RSP) task pane is used to define an optimization problem?

Which type of spreadsheet cell represents the decision variables in an LP model?

The English-reading eye scans

Which of the following describes Data Envelopment Analysis (DEA).

Spreadsheet modeling is an acquired skill because

The "Objective Value of" option in the Risk Solver Platform (RSP) task pane may be used to

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Sensitivity Analysis and the Simplex Method

Network Modeling

Integer Linear Programming

Goal Programming and Multiple Objective Optimization

Nonlinear Programming and Evolutionary Optimization

Regression Analysis

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

Exam 3: Modeling and Solving Lp Problems in a Spreadsheet

Which tab in the Risk Solver Platform (RSP) task pane is used to define an optimization problem?

Which type of spreadsheet cell represents the decision variables in an LP model?

The English-reading eye scans

Which of the following describes Data Envelopment Analysis (DEA).

Spreadsheet modeling is an acquired skill because

The "Objective Value of" option in the Risk Solver Platform (RSP) task pane may be used to

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Sensitivity Analysis and the Simplex Method

Network Modeling

Integer Linear Programming

Goal Programming and Multiple Objective Optimization

Nonlinear Programming and Evolutionary Optimization

Regression Analysis

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters