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.)