Kathleen Taylor has been working for a government contractor, Summit Solutions, in Washington, DC, for over a year. She is now eligible to participate in the company€™s 401(k) retirement plan. The company has provided Kathleen with the information in the table on the following page about the various funds that are available for her to invest in.

International funds invest in global/overseas companies; small-cap funds invest in companies that have a market capitalization (i.e., the number of outstanding shares multiplied by the stock price per share), in general, between $300 million and $2 billion; mid-cap funds invest in companies with a market capitalization between $2 and $10 billion; and large-cap funds invest in companies over $10 billion. The Evening Star rating is developed by an independent investment analysis firm, and it rates funds based on their risk-adjusted performance over various time periods. "5" is best, "1" is worst; stocks trading close to their analysts' fair value estimates receive a "3", while stocks trading at large discounts compared to their analysts' fair value estimate receive a "4" or "5" rating. The expense ratio is the total percentage of fund assets used for operating expenses (i.e., administrative, management, advertising, etc.).
Since Kathleen is young and expects to build her 401(k) plan over a long period of time, she wants to employ a relatively aggressive investment strategy. She has read investment literature that suggests a relatively aggressive plan would invest 5% to 35% in international funds, 5% to 25% in small-cap funds, 5% to 35% in mid-cap funds, 20% to 50% in large-cap funds, and 5% to 10% in bond funds. Kathleen plans to contribute $900 of her salary each month to her plan, which the company will match. She has also developed a few of her own investment guidelines: to diversify, she wants to invest in five funds, one in each investment category; she wants to achieve an average Evening Star rating of at least 3.7; she wants to invest in funds that average at least $10,000 million in size; she wants to achieve an average expense ratio for her five funds of no more than 1.10; and she wants to maximize the average 5-year return of the five funds she selects, weighted by the amount she invests in each.
Develop an investment plan for Kathleen using linear programming. How would her investment plan change if she wanted to maximize the Evening Starrating?

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Evening Star 5-Year Fud Size Expense Rating Return (S1,000,000s) Ratio 1.67 1.97 Parham International Value 7 Admiral Foreign Investor 1.32 U.S. Small Cap Select Veritas Smal Cap Value Federal Mid Cap Growth Draper Structured Mid Cap Maxam Mid Cap Opportunity T. Row Price Bluechip Growth Draper Strategic Growth 1.05 5 Centennial Common Stock Growth Madison Federated Bond Portfoli Draper U.S. Govemment Bond