First Securities, Inc., an investment firm, has $380,000 on account. The chief investment officer would like to reinvest the $380,000 in a portfolio that would maximize return on investment while at the same time maintaining a relatively conservative mix of stocks and bonds. The following table shows the investment opportunities and rates of return. Investment Opportunity Rate of Return Municipal Bonds (X1) 0.095 High Tech Stock (X2) 0.146 Blue Chip Stock (X3) 0.075 Federal Bonds (X4) 0.070 a) The Board of Directors has mandated that at least 60 percent of the investment consist of a combination of municipal and federal bonds, at least 25 percent Blue Chip Stock, no more than 30 percent High Tech and Blue Chip Stock, and no more than 15 percent High Tech Stock. Based on above problem, how many constraints are in this problem? A) 3 B) 4 C) 5 D) 2 b) Based on part a, which of the following would be the most appropriate constraint in the linear programming problem? A) X1 + X4 ≤ 0.6 (X1 + X2 + X3 + X4) B) X2 + X3 > 0.3 (X1 + X2 + X3 + X4) C) X1 + X4 > 0.6 (X1 + X2 + X3 + X4) D) X3 ≤ 0.25 (X1 + X2 + X3 + X4) c) Based on part a, which of the following would be the most appropriate constraint for the 30 percent High Tech and Blue Chip Stock investment?
First Securities, Inc., an investment firm, has $380,000 on account. The chief investment officer would like to reinvest the $380,000 in a portfolio that would maximize return on investment while at the same time maintaining a relatively conservative mix of stocks and bonds. The following table shows the investment opportunities and rates of return. Investment Opportunity Rate of Return Municipal Bonds (X1) 0.095 High Tech Stock (X2) 0.146 Blue Chip Stock (X3) 0.075 Federal Bonds (X4) 0.070 a) The Board of Directors has mandated that at least 60 percent of the investment consist of a combination of municipal and federal bonds, at least 25 percent Blue Chip Stock, no more than 30 percent High Tech and Blue Chip Stock, and no more than 15 percent High Tech Stock. Based on above problem, how many constraints are in this problem? A) 3 B) 4 C) 5 D) 2 b) Based on part a, which of the following would be the most appropriate constraint in the linear programming problem? A) X1 + X4 ≤ 0.6 (X1 + X2 + X3 + X4) B) X2 + X3 > 0.3 (X1 + X2 + X3 + X4) C) X1 + X4 > 0.6 (X1 + X2 + X3 + X4) D) X3 ≤ 0.25 (X1 + X2 + X3 + X4) c) Based on part a, which of the following would be the most appropriate constraint for the 30 percent High Tech and Blue Chip Stock investment?
Chapter12: Sequences, Series And Binomial Theorem
Section12.3: Geometric Sequences And Series
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First Securities, Inc., an investment firm, has $380,000 on account. The chief investment officer would like to reinvest the $380,000 in a portfolio that would maximize return on investment while at the same time maintaining a relatively conservative mix of stocks and bonds. The following table shows the investment opportunities and rates of return.
|
Investment Opportunity
|
Rate of Return
|
|
Municipal Bonds (X1) |
0.095 |
|
High Tech Stock (X2) |
0.146 |
|
Blue Chip Stock (X3) |
0.075 |
|
Federal Bonds (X4) |
0.070 |
- a) The Board of Directors has mandated that at least 60 percent of the investment consist of a combination of municipal and federal bonds, at least 25 percent Blue Chip Stock, no more than 30 percent High Tech and Blue Chip Stock, and no more than 15 percent High Tech Stock.
Based on above problem, how many constraints are in this problem?
- A) 3
- B) 4
- C) 5
- D) 2
- b) Based on part a, which of the following would be the most appropriate constraint in the linear programming problem?
- A) X1 + X4 ≤ 0.6 (X1 + X2 + X3 + X4)
- B) X2 + X3 > 0.3 (X1 + X2 + X3 + X4)
- C) X1 + X4 > 0.6 (X1 + X2 + X3 + X4)
- D) X3 ≤ 0.25 (X1 + X2 + X3 + X4)
- c) Based on part a, which of the following would be the most appropriate constraint for the 30 percent High Tech and Blue Chip Stock investment?
- A) -0.3X1 + 0.7X2 + 0.7X3 - 0.3X4 < 0
- B) 0.4X1 - 0.6X2 - 0.6X3 + 0.4X4 > 0
- C) - 0.25X1 - 0.25X2 + 0.75X3 - 0.25X4 > 0
- D) - 0.15X1 + 0.85X2 - 0.15X3 - 0.15X4 < 0
- d) Based on part a, what is the optimum solution to invest (how much) in Municipal Bond?
(A) 0
(B) 19000
(C) 95000
(D) 266000
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