Problem 11-3

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.

LetI	= Internet fund investment in thousands
B	= Blue Chip fund investment in thousands

If required, round your answers to two decimal places.

- 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	0

(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.

Internet Fund	=	$
Blue Chip Fund	=	$
Annual Return	=	$

Problem 11-5

Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows:

Rental Class
Super Saver	Deluxe	Business
Room	Type I	$30	$35	-
Type II	$20	$30	$40

Type I rooms do not have high-speed wireless Internet access and are not available for the Business rental class. Round Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 130 rentals in the Super Saver class, 60 in the Deluxe class, and 50 in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms.

(a)

Formulate and solve a linear program to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types.

Rental Class with room type	No of Reservations
Super Saver rentals allocated to room type I
Super Saver rentals allocated to room type II
Deluxe rentals allocated to room type I
Deluxe rentals allocated to room type II
Business rentals allocated to room type II

(b)

For the solution in part (a), how many reservations can be accommodated in each rental class?

Rental Class	No of Reservations
Super Saver I
Deluxe
Business

Demand for- Select your answer -DeluxeSuper SaverBusinessItem 9rental class was not satisfied.

(c)

With a little work, an unused office area could be converted to a rental room. If the conversion cost is the same for both types of rooms, would you recommend converting the office to a Type I or a Type II room?

Type I	Type II
Shadow Price	$	$

Convert an unused office area to- Select your answer -Type IType IIItem 12room.

Explain.