Question

Adirondack Savings Bank (ASB) has $1 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 5% for home loans, 13% for personal loans, and 8% for automobile loans. The bank’s planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans.

(a)	Formulate a linear programming model that can be used to determine the amount of funds ASB should allocate to each type of loan to maximize the total annual return for the new funds. If the constant is "1" it must be entered in the box. If your answer is zero enter “0”.
	Let H = amount allocated to home loans P = amount allocated to personal loans A = amount allocated to automobile loans
	Max H + P + A s.t. H + P + A ≥ Minimum Home Loans H + P + A ≤ Personal Loan Requirement H + P + A = Amount of New Funds
(b)	How much should be allocated to each type of loan?
	Loan type Allocation Home $ Personal $ Automobile $
	What is the total annual return?
	If required, round your answer to nearest whole dollar amount.
	$
	What is the annual percentage return?
	If required, round your answer to two decimal places.
	%
(c)	If the interest rate on home loans increases to 9%, would the amount allocated to each type of loan change?
	- Select your answer -YesNoItem 21
	Explain.
	The input in the box below will not be graded, but may be reviewed and considered by your instructor.
(d)	Suppose the total amount of new funds available is increased by $10,000. What effect would this have on the total annual return? Explain.
	If required, round your answer to nearest whole dollar amount.
	An increase of $10,000 to the total amount of funds available would increase the total annual return by $ .
(e)	Assume that ASB has the original $1 million in new funds available and that the planning committee has agreed to relax the requirement that at least 40% of the new funds must be allocated to home loans by 1%. How much would the annual return change?
	If required, round your answer to nearest whole dollar amount.
	$
	How much would the annual percentage return change?
	If required, round your answer to two decimal places.
	%

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). Maximize H+P+A such that

1*H + 1*P + 1*A = 1,000,000

1*H + 0*P + 0*A >= 40,000

1*P <= 0.06*A

H, P, A >= 0

Screenshot of the LP:

Get External Data Connections Data Tools Sort & Filter Solver Parameters B5 B C D Set Objective: SBSS To: O Max Min O Value of: Home loan Personal I Automobile loan 5% 13% 8% 400000 225000 375000 1000000 7.93% By Changing Variable Cells: $B$4:$D$4 79250 3 Annual return (%) 4 Amount 5 Total %age return 6 Total annual return 7 Constraints: 8 H+P+A = 1,000,000 9 H>=40% of new funds 10 PC 60%*A 11 H, P, A>=0 1000000 = 400000 >= 225000 1000000 400000 225000 Subject to the Constraints: $B$10 <= $D$10 $B$4:$D$4 >= 0 SBS8 = $D$8 $B$9 >= $D$9 Add Change Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method: GRG Nonlinear Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth.

b). Loan allocation:

Home loan = 400,000; personal loan = 225,000; automobile loan = 375,000

Total annual return = 79,250

Annual percentage return = 7.93%

c). No. Even if the interest rate on home loan increases to 9%, the allocated amount will not change because it is still less than the maximum rate being offered which is 13% on personal loan.

d). If new funds is increased by 10,000 then annual return will be 80,043. So, increase in total annual return = 80,043 - 79,250 = 793

e). New result of LP:

B C D E = N Home loan Personal I Automobile loan 5% 13% 8% 410000 221250 368750 1000000 7.88% 78763 Annual return (%) Amount 5 Total %age return 6 Total annual return 7 Constraints: 8 H+P+A= 1,000,000 9 H>=41% of new funds 10 PC= 60%*A 11 H, P, A>=0 1000000 = 410000 >= 221250 S 1000000 410000 221250

Annual return changes by 78,763 - 79,250 = -487

%age return changes by 7.88% - 7.93% = -0.05%