Blair & Rosen, Inc. (B&R;) is a brokerage firm that specializes in investment po

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 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 1 = Internet fund investment in thousands B = Blue Chip fund investment in thousands If required, round your answers to two decimal places Max 17 1 .07 Available investment funds 55 0 30 Maximum investment in the internet fund Maximum risk for a moderate investor 6 4 220 0

Explanation / Answer

Let the investment in Internet fund in thousands be I and Blue chip fund bin thousands be B

So, total investment=I+B

I+B<=55

Maximize Returns=I*17%+B*7%

At most 30000 in internet fund

so, I<=30

Risk rating=I*6+B*4

Maximum risk rating=220

So, I*6+B*4<=220

Hence,

1)

maximize I*17%+B*7%

s.t.

I<=30

I*6+B*4<=220

I+B<=55

I>=0

B>=0

Hence, I=30 and B=10

So, Investment in Internet fund=30000 and Investment in Blue Chip Fund=10000

Total return=0.17*30000+10000*0.07=5800

2)

maximize I*17%+B*7%

s.t.

I<=30

I*6+B*4<=310

I+B<=55

I>=0

B>=0

Hence, I=30 and B=25

So, investment in Internet fund=30000 and Blue chip fund=25000

Annual return=30000*0.17+25000*0.07=6850

3)

maximize I*17%+B*7%

s.t.

I<=30

I*6+B*4<=150

I+B<=55

I>=0

B>=0

Hence, I=25 and B=0

So, investment in Internet fund=25000 and Blue chip fund=0

Annual return=25000*0.17+0*0.07=4250

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