The Heinlein and Krampf Brokerage firm has just been instructed by one of its cl
ID: 2697600 • Letter: T
Question
The Heinlein and Krampf Brokerage firm has just been instructed by one of its clients to invest $250,00 of her money obtained recently through the land holdings in Ohio. The client has a good deal of trust in the investment house, but she also has her own ideas about the distribution of the funds being invested. In particular, she requests that the firm select whatever stocks and bonds they believe are well rated, but within the following guidelines:
a) Municipal bonds should constitute at least 20% of the investment.
b) At least 40% of the funds should be placed in a combination of electronic firms, aerospace firms, and drug manufacturers.
c) No more than 50% of the amount invested in municipal bonds should be placed in a high-risk, high yeild nursing home stock.
Subject to these restraints, the client's goal is to maximize projected return on investments. The analyst at Heinlein and Krampf, aware of the guidelines, prepare a list of high quality stocks and bonds and their corresponding rates of return:
INVESTMENT PROJECTED RATE OF RETURN(%)
LOS ANGELES MUNICIPAL BONDS 5.3
THOMPSON ELECTRONICS, INC 6.8
UNITED AEROSPACE CORP. 4.9
PALMER DRUGS 8.4
HAPPY DAYS NURSING HOMES 11.8
A) Formulate this portfolio selection problem using Linear Programming
B) Solve this problem
Explanation / Answer
a) Formulate this portfolio selection problem using LP. (b) Solve this problem.
Let X1 = dollars invested in Los Angeles municipal bonds
X2 = dollars invested in Thompson Electronics
X3 = dollars invested in United Aerospace
X4 = dollars invested in Palmer Drugs
X5 = dollars invested in Happy Days Nursing Homes
Maximize
.053X1
+
.068X2
+
.049X3
+
.084X4
+
.118X5
(maximize return on investment)
Subject to:
X1
+
X2
+
X3
+
X4
+
X5
?
250,000
(total funds available)
.8X1
-
.2X2
-
.2X3
-
.2X4
-
.2X5
?
0
(municipal bond restriction)
-.4X1
+
.6X2
+
.6X3
+
.6X4
-
.4X5
?
0
(electronics, aerospace, drugs combo)
-.5X1
+
X5
?
0
(nursing home as a percent of bonds)
X1, X2, X3, X4, X5
?
0
(non-negativity constraints)
Optimal Solution: X1 = $50,000 X2 = $0 X3 = $0 X4 = $175,000 X5 = $25,000 ROI = $20,300
Maximize
.053X1
+
.068X2
+
.049X3
+
.084X4
+
.118X5
(maximize return on investment)
Subject to:
X1
+
X2
+
X3
+
X4
+
X5
?
250,000
(total funds available)
.8X1
-
.2X2
-
.2X3
-
.2X4
-
.2X5
?
0
(municipal bond restriction)
-.4X1
+
.6X2
+
.6X3
+
.6X4
-
.4X5
?
0
(electronics, aerospace, drugs combo)
-.5X1
+
X5
?
0
(nursing home as a percent of bonds)
X1, X2, X3, X4, X5
?
0
(non-negativity constraints)
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.