Qutitative Assignmente 3 Ansewre

Quantitative Analysis for Decision Making
Assignment 3
Instruction
 Dear student, you will have to options to access and submit your assignment: either e-
learning portal or MS- office teams. You can use the students’ quick guides about these
platforms in order to understand how to use.
 Personal e-mailing will not be considered
 Submission date will be before and only on June 27, 2020
 No extension of deadline
Part One. Discussion Questions
1. What is post optimality or sensitivity analysis?

2. How sensitivity analysis helps the manager in making a Decision?
3. Discuss shadow price, range of optimality and range of feasibility.
Part two. Workout
1. An individual investor has Birr 70,000 to divide among several investments. The alternative
investments are municipal bonds with an 8.5% return, certificates of deposits with a 10%
return, Treasury bill with a 6.5% return, and income bonds with a 13% return. The amount of
time until maturity is the same for each alternative. However, each investment alternative has
a different perceived risk to the investor; thus it is advisable to diversify. The investor wants
to know how much to invest in each alternative in order to maximize the return. The
following guidelines have been established for diversifying the investment and lessening the
risk perceived by the investor.
No more than 20% of the total investment should be in an income bonds.
The amount invested in certificates of deposit should not exceed the amount invested
in other three alternatives.
At least 30% of the investment should be in treasury bills and certificates of deposits.
The ratio of the amount invested in municipal bonds to the amount invested in
treasury bills should not exceed one to three.
The investor wants to invest the entire Birr 70,000
Required:
 Formulate a LP model for the problem.

 Solve using the simplex method.
2. A manager of a firm that assembles various electronic items wants to establish an optimal
production plan for making Tape decks. The manager has obtained the pertinent information
which is shown in the table below:
Item Assembly Inspection Packaging cost per Price per

time time time unit unit
Type A 3 5 2 65 90
Type B 4 4 4 70 110
Type C 2 4 5 50 85
Available 60 hours 72 hours 96 hours
time
Required
a. Formulate the above LPP if the manager wants to maximize the total contribution of the
output to profit.
b. Write the problem in standard form and develop the initial tableau.
c. Determine the optimal solution using simplex. Identify the variables that are in solution at
the optimum and their values.
d. Identify the shadow prices and interpret each shadow price.
Keep your distance, Check that

you are safe, Work remotely,
Measure your productivity each
day, Because Life will continue.
Part One. Discussion Questions
1.What is post optimality or sensitivity analysis?
In linearl programming,all model parameters are assumed to be constant: but in real life situations,
the decision environment is always dynamic.
Therfore ,it is important for the management to know how profit would be affected by an
increase or decrease in the resource level,by achange in the technological process, andby
change in the cost of row material.
Such an investigation is known as sensitivity analysis or post-optimality analysis. The

results of sensitivity analysis establish upper and lower and bounds for input parameter
values within which they can vary without causing violent changes in the current optial
solution.
The main gol of the management is to know how sensitive the solution is the orginal data..
2. How sensitivity analysis helps the manager in making a Decision?

Decision making is an integral part of operations management. It may be useful to a decision
maker to have some indication of how sensitive an alternative choice might be to the changes in
one or more of those values. Unfortunately, it is not possible to explore all the possible
combinations of all the variables in a typical problem. In spite of this, there are some elements that
a decision maker can use to assess the sensitivity of assumption probabilities. One of the tools
useful for the analysis in some decision making problems is sensitivity analysis. It provides a range
of feasibility over which the choice of alternative remains the same. Successful decision making
consists of several steps, the fi rst and most important being carefully defi ning the problem. Given
that linear problems can be extensive and complex, they are solved by using sophisticated
computer methods. This paper will present software solutions available for personal computers
(Lindo, POM). For a manager taking the decision, however, a solution model is only part of the
answer. Sensitivity analysis offers a better understanding of the problem, different effects of
limitations and “what if“ questions. The insights obtained are frequently much more valuable that
a specifi c numerical answer. One of the advantages of linear programming lies in the fact that it
provides rich information on sensitivity analysis as a direct part of the solution.
Key words: feasibility range, linear programming, Lindo, POM, optimum solution, optimum range,
sensitivity analysis.
3. Discuss shadow price, range of optimality and range of feasibility.
Shadow Price
 Graphically, a shadow price is
determined by adding +1 to the
right hand side value in
question and then resolving for
the optimal solution in terms of
the same two binding
constraints
 The shadow price for
nonbinding constraints is 0
 A negative shadow price
indicates that the objective
function will not improve if the
RHS
is increases
Shadow Price
Graphically, a shadow price is determined by adding +1 to the right hand side value in
question and then resolving for the optimal solution in terms of the same two binding
constraints The shadow price for nonbinding constraints is 0 A negative shadow price
indicates that the objective function will not improve if the RHSis increases
Range of Optimality
 Graphically, the limits of a range of optimality are found by changing the slope of the
objective function line within the limits of the slopes of the binding constraint lines
 Slope of an objective function line, Max c
1
x
1
+c
2
x
2
, is -c
1
/c
2
, and the slope of a
constraint, a
1
x
1
+a
2
x
2
= b, is -a
1
/a
2
.
Range of Optimality
1
x
1
+c
2
x
2
, is -c
1
/c
2
constraint, a
1
x
1
+a
2
x
2
= b, is -a
1
/a
2
.
Range of Optimality
1
x
1
+c
2
x
2
, is -c
1
/c
2
constraint, a
1
x
1
+a
2
x
2
= b, is -a
1
/a
2
.
Range of Optimality
1
x
1
+c
2
x
2
, is -c
1
/c
2
constraint, a
1
x
1
+a
2
x
2
= b, is -a
1
/a
2
.
Range of Optimality
Graphically, the limits of a range of optimality are found by changing the slope of the
objective function line within the limits of the slopes of the binding constraint lines Slope
of an objective function line, Max c1x1 + c2x2, is -c1/c2, and the slope of a constraint, a1x1
+ a2x2 = b, is -a1/a2.
Range of Feasibility
The range of feasibility for a change in the right hand side value is the range of values
forthis coefficient in which the original dual price remains constant Graphically, the range
of feasibility is determined by finding the values of a right hand side coefficient such that
the same two lines that determined the original solution continue to determine the optimal
solution for the problem.
Part two. Workout
3. An individual investor has Birr 70,000 to divide among several investments. The alternative
investments are municipal bonds with an 8.5% return, certificates of deposits with a 10%
return, Treasury bill with a 6.5% return, and income bonds with a 13% return. The amount of
time until maturity is the same for each alternative. However, each investment alternative has
a different perceived risk to the investor; thus it is advisable to diversify. The investor wants
to know how much to invest in each alternative in order to maximize the return. The
following guidelines have been established for diversifying the investment and lessening the
risk perceived by the investor.
No more than 20% of the total investment should be in an income bonds.
The amount invested in certificates of deposit should not exceed the amount invested
in other three alternatives.
At least 30% of the investment should be in treasury bills and certificates of deposits.
The ratio of the amount invested in municipal bonds to the amount invested in
treasury bills should not exceed one to three.

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Quantitative Analysis for Decision Making

Part One. Discussion Questions

1. What is post optimality or sensitivity analysis?

Part two. Workout

 Formulate a LP model for the problem.

Item Assembly Inspection Packaging cost per Price per

Keep your distance, Check that

1.What is post optimality or sensitivity analysis?

Such an investigation is known as sensitivity analysis or post-optimality analysis. The

2. How sensitivity analysis helps the manager in making a Decision?

3. Discuss shadow price, range of optimality and range of feasibility.

Part two. Workout

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