Question

In: Statistics and Probability

HOMNEWORK 10 An investor wants to invest up to $100,000 as follows: X amount into a...

HOMNEWORK 10

An investor wants to invest up to $100,000 as follows:

X amount into a Certificate of Deposit (CD) that yields an expected annual return of 2% with a risk index of 1,

Y amount into a Bond with an expected annual return of 3% and a risk index of 4,

Z amount into a Stock with an expected annual return of 5% and a risk index of 8.

The investor’s objective is to maximize the total expected annual return of the investment.

However, to be prudent, the investor requires that:

The fraction of the total investment in X must be at least 40%.

The fraction of the total investment in Z must not exceed 30%.

The combined portfolio risk index must not exceed 5.

10.1 (10 points) Set up this investment problem as a linear program, which has 3 variables, 2 basic constraints and 4 general constraints.

10.2 (5 points) Use an LP software to find the maximum expected annual return in dollars and the dollar values of X, Y, and Z for this best investment.

10.3 (5 points) From the software solution, show the values of the dual variables for the four general constraints.

Expert Solution

the amount to be invested in three funds is 428571 and z is 571429 and return on investment is 37143$ .

orchestra answered 2 years ago

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