Question

Problem 7-27 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. What is the recommended investment portfolio for this client? What is the annual return for the portfolio? When required, round your answers to the nearest dollar. Internet fund Blue Chip fund Annual return b. 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? When required, round your answers to the nearest dollar. C. 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 an amount is zero, enter "O". When required, round your answers to the nearest dollar. Internet fund Blue Chip fund Annual return Discuss the interpretation of the slack variable for the total investment fund constraint. The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Answer 1

Let x1.x2 be the decision variables

where x1 is the amount invested in Internet fund and x2 is the amount invested in Blue chip funds.

Objective function : Max z =0.12*x1+0.09*x2

In excel ,

Annual return =B12=SUMPRODUCT(B3:B4,B8:B9)=$ 5100

Constraints :

B15=SUM(B8:B9)

B16=B8

B17=(6*B8+4*B9)/1000

Calculations are as shown below :

Internet fund = $ 20000

Blue chip fund = $ 30000

Annual return=$ 5100

SUMPRODUCT(B3:B4,B8:B9) B12 Solver Parameters Set Target Cell: Equal To: o Max By Changing Cells: 2 Type of fund Return 3 Internet fund 4 Blue chip fund 5B$12 0.12 (。Min C) Value of: O 0.09 $B$8:$B$9 6 Variable cells 7 Type of fund Amount to invest(S) 8 Internet fund 9 Blue chip fund 10 11 Objective func 12 Annual return 13 14 Constraints 15 C1 16 C2 17 C3 Subject to the Constraints: Options $8$16$D$16 SB$17 <$D$17 Reset All Delete 5100 50000 20000仁 35000 240 <= 240

b.In this case ,constraint C3 will be changed and in excel D17=160 and solving the problem again using solver ,we get

B12 Solver Parameters 2 Type of fund Return 3 Internet fund 4 Blue chip fund Set Target Cell: BS12 Equal To: o Max (。Min By Changing Cells: 0.12 C) Value of: 0.09 $8$8:$8$9 6 Variable cells 7 Type of fund Amount to invest(S) 8 Internet fund 9 Blue chip fund 10 11 Objective func 12 Annual return 13 14 Constraints 15 C1 16 C2 17 C3 Subject to the Constraints: Options SB$15 D$15 $B$16$D$16 $8$17 <= $D$17 Reset All Delete 3600 40000- 50000 35000 160 160 <-

Internet fund = $ 0

Blue chip fund = $ 40000

Annual return=$ 3600

(Not a feasible solution though ,because constraint C1 is not satisfied)

The slack variable for the total investment fund constraint is not zero in this case.This indicates that there is non utilized resource or slack resource.In this case ,slack resource for constraint is 10000.

i.e there is still $ 10000 of investment that has not been used.