Question

Question: Blair & Rosen, Inc. (B&R) is a brokerage firm that specializes in investment portfolios d...

Blair & Rosen, Inc. (B&R) is a brokerage firm that specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client who contacted B&R this past week has a maximum of $55,000 to invest. B&R's investment advisor decides to recommend a portfolio consisting of two investment funds: an Internet fund and a Blue Chip fund. The Internet fund has a projected annual return of 11%, while the Blue Chip fund has a projected annual return of 7%. The investment advisor requires that at most $25,000 of the client's funds should be invested in the Internet fund. B&R services include a risk rating for each investment alternative. The Internet fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per thousand dollars invested. The Blue Chip fund has a risk rating of 4 per thousand dollars invested. For example, if $10,000 is invested in each of the two investment funds, B&R's risk rating for the portfolio would be 6(10) + 4(10) = 100. Finally, B&R developed a questionnaire to measure each client's risk tolerance. Based on the responses, each client is classified as a conservative, moderate, or aggressive investor. Suppose that the questionnaire results classified the current client as a moderate investor. B&R recommends that a client who is a moderate investor limit his or her portfolio to a maximum risk rating of 230.

(a)	Formulate a linear programming model to find the best investment strategy for this client.
	Let I = Internet fund investment in thousands B = Blue Chip fund investment in thousands
	If required, round your answers to two decimal places. If an amount is zero, enter “0”. If the constant is "1" it must be entered in the box.
	- Select your answer -MaxMinItem 1 I + B s.t. I + B ≤ Available investment funds I + B ≤ Maximum investment in the internet fund I + B ≤ Maximum risk for a moderate investor I, B ≥
(b)	Build a spreadsheet model and solve the problem using Solver. What is the recommended investment portfolio for this client?
	Internet Fund = $ Blue Chip Fund = $
	What is the annual return for the portfolio?
	$
(c)	Suppose that a second client with $55,000 to invest has been classified as an aggressive investor. B&R recommends that the maximum portfolio risk rating for an aggressive investor is 350. What is the recommended investment portfolio for this aggressive investor?
	Internet Fund = $ Blue Chip Fund = $ Annual Return = $
(d)	Suppose that a third client with $55,000 to invest has been classified as a conservative investor. B&R recommends that the maximum portfolio risk rating for a conservative investor is 170. Develop the recommended investment portfolio for the conservative investor. If an amount is zero, enter “0”.
	Internet Fund = $ Blue Chip Fund = $ Annual Return = $

Answer 1

a)

Formulate the linear programming model to find the best investment stratgey

I=internet fund investment

B=blue Chip fund investment

It has been given that

The Internet fund has a projected annual return of 11%=0.11 let us take variable I

while the Blue Chip fund has a projected annual return of 7%=0.07 let us take variable B

Formulation will be

Maximize=(annual return)

0.111+0.07

Subject to

$I+B\leq 55,000$(maximum investment amount)

Because  maximum of $55,000 to invest.

$I\leq 25,000$(Internet invvestment fund)

$0.006I+0.004B\leq 230$(Risk Rating)

$I,B\geq 0$(Non -Negative Constrain)

b)

	I	B	annual return
Investment portfolio	25000	20000	4150
annual return	0.11	0.07
Constrains			Used resource	sign	Utilized
Maximum investment amount	1	1	45000	≤	55000
Internet investment amount	1	0	25000	≤	25000
risk rating	0.006	0.004	230	≤	230

Formula which will be used

	I	B	annual return
Investment portfolio	25000	20000	=SUMproduct(B2:C2,B3:C3)
annual return	0.11	0.07
Constrains			Used resource	sign	Utilized
Maximum investment amount	1	1	=SUMproduct($B$2:$C$2,B5:C5)	≤	55000
Internet investment amount	1	0	=SUMproduct($B$2:$C$2,B6:C6)	≤	25000
risk rating	0.006	0.004	=SUMproduct($B$2:$C$2,B7:C7)	≤	230

We will use the Simplex Linear programming method for finding

Set Objective To: By Changing Variable Cells: Subject to the Constraints: Add Change Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method: Simplex LP Optons Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth noninear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth

Internet fund=25000

Blue chip fund=20,000

Annual return=4150

c)

Internet Fund=$25,000

Blue Chip Fund=$30,000

Annual Return=$4850

	I	B	annual return
Investment portfolio	25000	30,000	4850
annual return	0.11	0.07
Constrains			Used resource	sign	Utilized
Maximum investment amount	1	1	55000	≤	55000
Internet investment amount	1	0	25000	≤	25000
risk rating	0.006	0.004	270	≤	230

d)

Internet Fund=$25,000

Blue Chip Fund=$5,000

Annual Return=$3100

	I	B	annual return
Investment portfolio	25000	5,000	3100
annual return	0.11	0.07
Constrains			Used resource	sign	Utilized
Maximum investment amount	1	1	30000	≤	30000
Internet investment amount	1	0	25000	≤	25000
risk rating	0.006	0.004	170	≤	170