Message to Tutor: I will use Excel Solver for this question. I am totally lost on how to formulate the Objective Function Z: I provided an example of the information I would use to enter into Excel Solver for your reference: This question involves linear programming

Decision Variables

Trial Values

Objective Function Z

Constraints

Constraints

Question: Consider the case of 20th Century Funds, Inc. located in Washington D.C. Century decided to invest in a portfolio for a client. Based on prior experience and other information, the financial manager recommended a portfolio of six assets including cash. In coordination with the client, the broker decided on the following list of financial assets.

Number Investment Type Investment holding period Annual Return(%) Risk Measure Growth Potential (%)

1 3 month treasury bill 3 1.7 1 2

2 Russel 3000 Index 5 28 290 10

3 US 10 year bond 7 2 19 3

4 Russel 1000 growth index 9 34 285 12

5 One year saving 4 1.8 15 2

6 Cash 0 0 0 0

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The financial manager at Century would like to maximize the return on the portfolio investments for his client with the following restrictions.

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

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

3.The overall growth potential for the portfolio must be at least 10 percent

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

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

Question: Use the information given in the question to formulate the Linear Programming problem.

Make sure you show the objective function and the constraints defining all the relevant variables.