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 Drespectively.1.(b) Now, the objective function is to minimize the total risk. The price per share is given and therisk 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 havemin Risk = 10a + 3.56 + 4c+ 3.2d1.(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 = 2000002. 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 numberof shares multiplied by the price per share, so based on this we get12a + 4b + 4.8c+ 4d > 180003. 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 equations100a < 100000, 506 < 100000, 80c < 100000, 40d < 100000= a < 1000, b< 2000, c< 1250, d < 25004. The total investment in A and B must be equal to or greater than the total investment in C andD, so100a + 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 infour specific stocks - A, B, C, and/or D. The company gathered the following relevant financialdata for the four stocks:Stock CStock AStock BStock DPrice per shareS100$50S80$40Annual rate of0.120.080.060.10returnRisk measure0.100.070.050.08per dollarinvestedBased 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 morethan 50% of the total dollar investment.4. The total investment in stocks A and B combined must be equal to or greater than the totalinvestment in stocks C and D combined.

We will use linear optimization to solve this question. Note that your constraints are already…

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.

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

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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

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.

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