An investment company manages portfolios of stocks, bonds, and other investment alternatives. One of the company's clients would like to invest $200,000 in stocks. The client is interested in four specific stocks - A, B, C, and/or D. The company gathered the following relevant financial data for the four stocks: Stock A S100 0.12 Stock B S50 0.08 Stock C Price per share Annual rate of Stock D $40 0.10 S80 0.06 return Risk measure 0.10 0.07 0.05 0.08 per dollar invested Based on the above data, the investor has stipulated the following investment guidelines: 1. The entire amount of $200,000 must be invested. 2. The annual rate of return must be at least 9% of the invested capital of $200,000. 3. Not every stock has to be purchased, however, if selected, no one stock can account for more than 50% of the total dollar investment. 4. The total investment in stocks A and B combined must be equal to or greater than the total investment in stocks C and D combined.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

Q3.  What are the objective coefficient ranges for the four stocks? Show the relevant portion of the Solver’s output. Fully interpret these ranges.

1.(a) Let a, b, c, d be the decision variables representing the number of shares of stocks A,B,C and D
respectively.
1.(b) Now, the objective function is to minimize the total risk. The price per share is given and the
risk measure per dollar invested is given, so we can multiply them to get the risk measure per share,
and then use it for our objective function. So we have
min Risk = 10a + 3.56 + 4c+ 3.2d
1.(c) Now we develop the constraints.
1. The entire amount of $200,000 must be invested so we must have, using the price per share given:
100a + 506 + 80c + 40d = 200000
2. The annual rate of return must be at least 9% of the invested capital of $200,000, that is, $18,000.
Now, we are given the annual rate of return on investment, and the total investment is the number
of shares multiplied by the price per share, so based on this we get
12a + 4b + 4.8c+ 4d > 18000
3. If selected, then each stock can account for no more than 50% of the total dollar investment, i.e.
$100,000. So we get four separate equations
100a < 100000, 506 < 100000, 80c < 100000, 40d < 100000
= a < 1000, b< 2000, c< 1250, d < 2500
4. The total investment in A and B must be equal to or greater than the total investment in C and
D, so
100a + 506 > 80c+ 40d → 10a + 56 – 8c – 4d > 0
Transcribed Image Text:1.(a) Let a, b, c, d be the decision variables representing the number of shares of stocks A,B,C and D respectively. 1.(b) Now, the objective function is to minimize the total risk. The price per share is given and the risk measure per dollar invested is given, so we can multiply them to get the risk measure per share, and then use it for our objective function. So we have min Risk = 10a + 3.56 + 4c+ 3.2d 1.(c) Now we develop the constraints. 1. The entire amount of $200,000 must be invested so we must have, using the price per share given: 100a + 506 + 80c + 40d = 200000 2. The annual rate of return must be at least 9% of the invested capital of $200,000, that is, $18,000. Now, we are given the annual rate of return on investment, and the total investment is the number of shares multiplied by the price per share, so based on this we get 12a + 4b + 4.8c+ 4d > 18000 3. If selected, then each stock can account for no more than 50% of the total dollar investment, i.e. $100,000. So we get four separate equations 100a < 100000, 506 < 100000, 80c < 100000, 40d < 100000 = a < 1000, b< 2000, c< 1250, d < 2500 4. The total investment in A and B must be equal to or greater than the total investment in C and D, so 100a + 506 > 80c+ 40d → 10a + 56 – 8c – 4d > 0
An investment company manages portfolios of stocks, bonds, and other investment alternatives.
One of the company's clients would like to invest $200,000 in stocks. The client is interested in
four specific stocks - A, B, C, and/or D. The company gathered the following relevant financial
data for the four stocks:
Stock C
Stock A
Stock B
Stock D
Price per share
S100
$50
S80
$40
Annual rate of
0.12
0.08
0.06
0.10
return
Risk measure
0.10
0.07
0.05
0.08
per dollar
invested
Based on the above data, the investor has stipulated the following investment guidelines:
1. The entire amount of $200,000 must be invested.
2. The annual rate of return must be at least 9% of the invested capital of $200,000.
3. Not every stock has to be purchased, however, if selected, no one stock can account for more
than 50% of the total dollar investment.
4. The total investment in stocks A and B combined must be equal to or greater than the total
investment in stocks C and D combined.
Transcribed Image Text:An investment company manages portfolios of stocks, bonds, and other investment alternatives. One of the company's clients would like to invest $200,000 in stocks. The client is interested in four specific stocks - A, B, C, and/or D. The company gathered the following relevant financial data for the four stocks: Stock C Stock A Stock B Stock D Price per share S100 $50 S80 $40 Annual rate of 0.12 0.08 0.06 0.10 return Risk measure 0.10 0.07 0.05 0.08 per dollar invested Based on the above data, the investor has stipulated the following investment guidelines: 1. The entire amount of $200,000 must be invested. 2. The annual rate of return must be at least 9% of the invested capital of $200,000. 3. Not every stock has to be purchased, however, if selected, no one stock can account for more than 50% of the total dollar investment. 4. The total investment in stocks A and B combined must be equal to or greater than the total investment in stocks C and D combined.
Expert Solution
steps

Step by step

Solved in 4 steps with 3 images

Blurred answer
Knowledge Booster
Transcendental Expression
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,