A portfolio manager in charge of a bank portfolio has $10 million to invest. The securities available for purchase, as well as their respective quality ratings, maturities, and yields, are shown in the table below:

The bank places the following policy limitations on the portfolio manager's actions:
1. Government and agency bonds must total at least $4 million.
2. The average quality of the portfolio cannot exceed 1.4 on the bank's quality scale. (Note that a low number on this scale means a high-quality bond.)
3. The average years to maturity of the portfolio must not exceed 5 years.
Assuming that the objective of the portfolio manager is to maximize after-tax earnings and that the tax rate is 50%, formulate a linear program that can be used to determine how much money to invest in each type of bond.

Question

A portfolio manager in charge of a bank portfolio has $10 million to invest. The securities available for purchase, as well as their respective quality ratings, maturities, and yields, are shown in the table below:
  
The bank places the following policy limitations on the portfolio manager's actions:
1. Government and agency bonds must total at least $4 million.
2. The average quality of the portfolio cannot exceed 1.4 on the bank's quality scale. (Note that a low number on this scale means a high-quality bond.)
3. The average years to maturity of the portfolio must not exceed 5 years.
Assuming that the objective of the portfolio manager is to maximize after-tax earnings and that the tax rate is 50%, formulate a linear program that can be used to determine how much money to invest in each type of bond.

Quizplus · Accepted Answer

The Answer of A portfolio manager in charge of a bank portfolio has $10 million to invest. The securities available for purchase, as well as their respective quality ratings, maturities, and yields, are shown in the table below:
  
The bank places the following policy limitations on the portfolio manager's actions:
1. Government and agency bonds must total at least $4 million.
2. The average quality of the portfolio cannot exceed 1.4 on the bank's quality scale. (Note that a low number on this scale means a high-quality bond.)
3. The average years to maturity of the portfolio must not exceed 5 years.
Assuming that the objective of the portfolio manager is to maximize after-tax earnings and that the tax rate is 50%, formulate a linear program that can be used to determine how much money to invest in each type of bond.

A Portfolio Manager in Charge of a Bank Portfolio Has