Question

Problem 11-3

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 17%, while the Blue Chip fund has a projected annual return of 7%. The investment advisor requires that at most $30,000 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 220.

(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.
	- Select your answer -MaxMinItem 1 I + B s.t. I + B - Select your answer -≤≥=Item 6 Available investment funds I + B - Select your answer -≤≥=Item 10 Maximum investment in the internet fund I + B - Select your answer -≤≥=Item 14 Maximum risk for a moderate investor I, B - Select your answer -≤≥=Item 16 0
(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 310. 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 150. Develop the recommended investment portfolio for the conservative investor.
	Internet Fund = $ Blue Chip Fund = $ Annual Return = $

Answer 1

ANSWER:

Given that,

This problem is a linear programming problem with two decision variables which are the amount to be invested in internet fund and the amount to be invested in Blue chi fund.We have to maximize the profit made from the investment ,Subjected to the constraints. This problem can be formulated in excel and can be solved using the solver module.

a)

Decision variables:

I=Amount invested in Internet fund

B=Amount invested in blue chip fund

A client who contacted B&R this past week has maximum of $55000 to invest.

I+B<=55000

The investment advisory requires that at most $30,000 of the clients funds should be invested in the internet fund.

I<=30000

b)

A client who is a moderate investor limits his or her portfolio to a maximum risk rating of 220.

(6/1000)*I+(4/1000)B<=220

Objective function:

Maximize Z=(17/100)*I+(7/100)*B

Solving the above linear programming using excel solver we get the optimum investment for maximum profit gain in the question.

Internet fund=I=0,

Blue chip fund+B=$55000

Annual return=$3840

c)

The second client is an aggressive investor and hence the question remains same except the third constraints which becomes:(6/1000)*I+(4/1000)*B<=310

Now we solve the equation we can get the values.

Internet fund=I=$45000

Blue chip fund=B=$10000

Annual return =$8350

Under the aggressive investor strategy the annual return increase from $3850 to $8350

d)

The third client is a conservative investor and hence the question remains same except the third constraint which now becomes:

(6/1000)*I+(4/1000)*B<=150

Internet fund=I=-$35000

Blue chip fund=B=$90000 Annual return=$350