### Formulate a linear goal programming model

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Ferris, an investment management firm located in New York, has recently been retained as the endowment fund manager for a small Midwestern college. The firm is attempting to determine a best investment portfolio for its client and has reduced overall consideration to six alternative investments to add to the college portfolio. Information for the investment choices includes point estimates for: price per share; annual growth in price per share; annual dividend per share; and a measure of the risk associated with each investment. In this case, risk is defined as the standard deviation in return. Dollar return per share of stock is defined as price per share one year hence less current price per share plus dividend per share.

Alternatives 1 2 3 4 5 6
Current price per share \$80.00 \$100.00 \$160.00 \$120.00 \$150.00 \$200.00

Projcted annl grwth rte 0.08 0.07 0.10 0.12 0.09 0.15

Projected annual-
dividend per share \$4.00 \$6.50 \$1.00 \$0.50 \$2.75 \$0.00

Projected risk 0.05 0.03 0.10 0.20 0.06 0.08

The endowment fund has \$2.5 million to invest and the college trustees, having reviewed the alternatives, wish to have the portfolio structured to adhere to certain conditions with the following ordered priorities:

· The portfolio should return at least 7.0% on the additional investment.

· The maximum dollar amount to be invested in alternative 6 should not exceed \$250,000.

· Not more than \$500,000 should be invested in alternatives 1 and 2 combined.

· Total weighted risk should not be greater than 10%*

· The portfolio should return at least \$10,000 in dividends annually.

· The amount invested in alternatives 1 and 2 combined should be at least 10% of the total funds invested in this process.

· Total weighted risk should not be greater than 1%*

* Total weighted risk is defined as:

(\$ invested in alternative i)(risk of alternative i))/(total \$ invested in all alternatives)

Question how do I Formulate a linear goal programming model that can be used to determine the selection of investment alternatives to include in the portfolio that will best satisfy the stated goal priorities established by the college trustees.

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