Question

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 $50,000 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 12%, while the Blue Chip fund has a projected annual return of 9%. The investment advisor requires that at most $35,000 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 240.

(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 the constant is "1" it must be entered in the box. If your answer is zero enter “0”.
	- 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
(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 $50,000 to invest has been classified as an aggressive investor. B&R recommends that the maximum portfolio risk rating for an aggressive investor is 320. What is the recommended investment portfolio for this aggressive investor?
	Internet Fund = $ Blue Chip Fund = $ Annual Return = $
(d)	Suppose that a third client with $50,000 to invest has been classified as a conservative investor. B&R recommends that the maximum portfolio risk rating for a conservative investor is 160. Develop the recommended investment portfolio for the conservative investor. If your answer is zero enter “0”.
	Internet Fund = $ Blue Chip Fund = $ Annual Return = $

Answer 1

a. Let the amount invested in internet fund be "I" and blue chip fund be "B".

Nowm we have to maximize the return for the portfolio. Portfolio return = weighted average return of the two funds = 0.12I+0.09B. This is the objective function and this will have to be maximized.

Constraints:

(i) I+B<=50,000 (maximum amount avaliable for investment)

(ii) I<=35,000 (at most $35,000 of the client's funds should be invested in the Internet fund)

(iii) 6/1000*I+4/1000*B<=240 (maximum risk for a moderate investor).

Solving in excel, using the solver function, the following solution is obtained:

b.

	Internet	Blue chip
Amount invested	20000	30000
Returns	0.12	0.09
Portfolio return	5100
Constraints				Formula
50000	<=	50000		I+B<=50,000
20000	<=	35000		I<=35000
240	<=	240		6/1000*I+4/1000*B<=240

Thus I = $20,000 and B = $30,000. Annual return = $5,100. All contraints are satisfied.

c. Constraint (i) and (ii) will remain the same. The 3rd constraint will become:  6/1000*I+4/1000*B<=320

Solving in excel, the following solution is obtained:

	Internet	Blue chip
Amount invested	35000	15000
Returns	0.12	0.09
Portfolio return	5550
Constraints				Formula
50000	<=	50000		I+B<=50,000
35000	<=	35000		I<=35000
270	<=	320		6/1000*I+4/1000*B<=320

I = $35,000. B = $15,000 and Annual Return = $5,500

d. Constraint (i) and (ii) will remain the same. The 3rd constraint will become:  6/1000*I+4/1000*B<= 160. Solution:

	Internet	Blue chip
Amount invested	0	40000
Returns	0.12	0.09
Portfolio return	3600
Constraints				Formula
40000	<=	50000		I+B<=50,000
0	<=	35000		I<=35000
160	<=	160		6/1000*I+4/1000*B<=320

I = $0, B = $40,000 and Annual return = $3,600.