20th Century Funds, Inc. decided to invest in a portfolio for a client from an upper-middle-class family. The financial manager is considering a portfolio of six assets including cash as shown below:

Number Investment Type Investment holding period Annual Return Risk measure Growth potential(%)

1 3 moth treasury bill 3 1.7 1 2

2 Russel 3000 5 28 290 10

3 US 10 year Bond 7 2 19 3

4 Russel 100 growth index 9 34 285 12

5 One year Saving 4 1.8 15 2

6 Cash 0 0 0 0

The financial manager would like to maximize the return on the portfolio investments for his client subject to the following constraints.

- The average length of the investment for the portfolio should not exceed 10 years.

- The average risk for the portfolio is at most 200.

- The overall growth potential for the portfolio must be at least 8 percent.

- The client requires the broker to maintain at least 8 percent of the total funds as cash.

- The total proportions of funds in the portfolio of all assets must add up to 1.0.

Formulate (DO NOT SOLVE) the linear program for this problem using the following decision variables:

X1 = proportion of funds invested in 3-month treasury bill

X2 = proportion of funds invested in Russel 3000 index

X3 = proportion of funds invested in US 10-year bond

X4 = proportion of funds invested in Russel 1000 growth index

X5 = proportion of funds invested in US credit union 1 year saving rate

X6 = proportion of funds invested in Cash

a) Formulate the objective function to maximize the total return for the portfolio.

b) Formulate the constraints as functions of the decision variables.

c) Formulate the constraints for the bounds (i.e,. non-negativity) on the decision variables.