DEVELOPING KATHLEEN TAYLOR'S 401(K) PLAN Kathlee athleen 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 following table about the various funds that are available for her to invest in. Evening Star Rating 5-Year Return Fund Size ($1,000,000s) Expense Ratio 3 4 2 5 3 12.58 6.94 7.86 7.54 5.57 2,066 7,404 19,859 42,035 11,139 1.67 1.97 1.19 1.32 1.15 4 2 4 3 5.87 3.99 2.97 3.8 1,302 770 3,049 4,320 1.43 1.21 1.74 1.49 International Parham International Value Jarus Overseas U.S. Fund Euro Pacific Admiral Foreign Investor SPS Emerging Market Small-Cap Maxam Small Cap Return U.S. Small Cap Select Veritas Small Cap Value Oak Small Cap Growth Mid-Cap Federal Mid Cap Growth T. Row Price Growth Draper Structured Mid Cap Jarus Mid Cap Value Maxam Mid Cap Opportunity Large-Cap T. Row Price Bluechip Growth Jarus Diversified Equity Income Draper Strategic Growth Centennial Common Stock Growth Marius Stock Growth Bond 729 3 2 2 3 4.13 6.30 7.73 4.05 5.76 4,145 1,467 4,632 2,537 1.05 1.33 1.31 1.52 1.17 4 3 2 4 3 2 6.01 3.22 7.81 2.16 6,374 962 9,991 20,194 19,648 1.23 1.05 1.16 0.99 1.12 9.88 3 Maxam Global Bond Parham High Yield Madison Federated Bond Portfolio Draper U.S. Government Bond Federated High Income 5 3 8.37 6.25 5.66 7.41 5.85 12,942 3,106 8,402 1,045 11,211 1.03 1.00 1.14 0.90 0.82 4 3 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 multi- plied 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, l 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 esti- mate 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). Because 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 percent in international funds, 5 to 25 percent in small-cap funds, 5 to 35 percent in mid-cap funds, 20 to 50 percent in large-cap funds, and 5 to 10 percent 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 invest- ment 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 aver- age 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 Star rating? DEVELOPING KATHLEEN TAYLOR'S 401(K) PLAN Kathlee athleen 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 following table about the various funds that are available for her to invest in. Evening Star Rating 5-Year Return Fund Size ($1,000,000s) Expense Ratio 3 4 2 5 3 12.58 6.94 7.86 7.54 5.57 2,066 7,404 19,859 42,035 11,139 1.67 1.97 1.19 1.32 1.15 4 2 4 3 5.87 3.99 2.97 3.8 1,302 770 3,049 4,320 1.43 1.21 1.74 1.49 International Parham International Value Jarus Overseas U.S. Fund Euro Pacific Admiral Foreign Investor SPS Emerging Market Small-Cap Maxam Small Cap Return U.S. Small Cap Select Veritas Small Cap Value Oak Small Cap Growth Mid-Cap Federal Mid Cap Growth T. Row Price Growth Draper Structured Mid Cap Jarus Mid Cap Value Maxam Mid Cap Opportunity Large-Cap T. Row Price Bluechip Growth Jarus Diversified Equity Income Draper Strategic Growth Centennial Common Stock Growth Marius Stock Growth Bond 729 3 2 2 3 4.13 6.30 7.73 4.05 5.76 4,145 1,467 4,632 2,537 1.05 1.33 1.31 1.52 1.17 4 3 2 4 3 2 6.01 3.22 7.81 2.16 6,374 962 9,991 20,194 19,648 1.23 1.05 1.16 0.99 1.12 9.88 3 Maxam Global Bond Parham High Yield Madison Federated Bond Portfolio Draper U.S. Government Bond Federated High Income 5 3 8.37 6.25 5.66 7.41 5.85 12,942 3,106 8,402 1,045 11,211 1.03 1.00 1.14 0.90 0.82 4 3 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 multi- plied 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, l 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 esti- mate 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). Because 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 percent in international funds, 5 to 25 percent in small-cap funds, 5 to 35 percent in mid-cap funds, 20 to 50 percent in large-cap funds, and 5 to 10 percent 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 invest- ment 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 aver- age 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 Star rating