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 $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 8%. 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 5 per thousand dollars invested. The Blue Chip fund has a risk rating of 5 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 5(10) + 5(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 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 - 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 $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 150. 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

Objective function:

The objective is to maximize the total return from the investment. The rate of return of the internet fund is 17% and that of blue chip fund is 8%. Thus total return on investment is given as follows:

Returns = (0.17)(amount invested in internet fund) + (0.08)(amount invested in blue chip fund) = (0.17*I) + (0.08*B)

The objective is to maximize the returns, thus the objective function is:

Max Z = 0.17*I + 0.08*B    

Subject to:

1. Maximum invest amount is $55,000

Total investment <= available investment

1*I + 1*B <= 55 (in thousands)

2. Maximum investment in internet fund is $25,000

1*I + 0*B <= 25 (in thousands)

3. Maximum risk for moderate investor is 240

Total portfolio risk <= maximum risk

5*I + 5*B <= 240

4. Non-negativity constraint

I, B >= 0

b)

Excel Model:

Optimal Solution:

Investment in Internet fund = $25 (in thousands)

Investment in Blue chip fund = $23 (in thousands)

Maximum returns = $6.09 (in thousands)

c)

the new risk constraint is: 5*I + 5*B <= 350

Resolve the Excel model by changing the RHS of risk constraint from 240 to 350

The optimal solution:

Investment in Internet fund = $25 (in thousands)

Investment in Blue chip fund = $30 (in thousands)

Maximum returns = $6.65 (in thousands)

Part d)

the new risk constraint is: 5*I + 5*B <= 150

Resolve the Excel model by changing the RHS of risk constraint from 240 to 150

The optimal solution:

Investment in Internet fund = $25 (in thousands)

Investment in Blue chip fund = $5 (in thousands)

Maximum returns = $4.65 (in thousands)