system modeling (information systems) help

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1.------- elements of the Linear Optimization. Please define and discuss the important elements and why are they important? Additionally, discuss the tools involved in Linear Optimization. Since this is a graded assignment please provide reference citations for information.

 

 

2.------- MANAGING A PORTFOLIO------ A local bank wants to build a bond portfolio from a set of four bonds with $1 million available for investment. The expected annual return, the worst-case annual return on each bond, and the "duration" of each bondare given in the following table.(The duration of a bond is a measure of the bond's sensitivity to changes in the interest rates.)

TABLE

                    Expected              worst case

                     Return                        Return                        Duration

Bond 1            12.5%                        8.0%                               8

 

Bond  2           11.5%                        7.5%                               7

 

Bond  3           10.5%                        6.8%                              6

 

Bond  4              9.5%                        7.0%                              5

 

Bond  5                8.5%                      7.4%                              3

The bank wants to maximize the expected return from its bond investments, subject to  three conditions.

1.---- The average worst-case return for the portfolio must be at least 7.2 percent.

2.--- The avereage duration of the portfolio must be at most 6.

3.---- Because of diversification requirements, at most 40 percent of the total amount invested can be invested in a single Bond.

 

Questions:

A.---- What is the maximum return on the $ 1 million investment? How should the investment be distributed among the bonds to achieve this return?(Assume that bonds can  be purchased in fractional amounts.)

 

B.----- What is the qualitative pattern in the optimal solution?

 

C.---What is the marginal rate of return on the investment amount? That is, what would be the percentage return on an additinal dollar invested?(Give the percentage to four significant figures.)

 

 

 

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