Michael Colella is the financial advisor for a number ofprofessional athletes. An analysis of the long-term goals for many of these athletes has resulted in a recommendation to purchase stocks with some of the income that they have set aside for investments. Michael has identified five stocks having very favorable expectations for future performance. Although the expected return is important in these investments, the risk, as measured by the beta of the stock, is also important. (A high value beta indicates that the stock has a relatively high risk.) The expected return and the beta for the five stocks are as follows:

Stock	DW	EE	HA	MC	ZM
Expected Return (%)	11.0	9.0	6.5	15.0	13.5
Beta	1.20	0.85	0.55	1.40	1.25

Michael would like to minimize the beta of the stock portfolio (calculated using a weighted average of the amounts put into the different stocks) while maintaining an expected return of at least 11%. Since future conditions may change, Michael has decided that no more than 35% of the portfolio should be invested in any one stock.

Michael Colella is the financial advisor for a number ofprofessional athletes. An analysis of the long-term goals for many of these athletes has resulted in a recommendation to purchase stocks with some of the income that they have set aside for investments. Michael has identified five stocks having very favorable expectations for future performance. Although the expected return is important in these investments, the risk, as measured by the beta of the stock, is also important. (A high value beta indicates that the stock has a relatively high risk.) The expected return and the beta for the five stocks are as follows:

Stock	DW	EE	HA	MC	ZM
Expected Return (%)	11.0	9.0	6.5	15.0	13.5
Beta	1.20	0.85	0.55	1.40	1.25

Michael would like to minimize the beta of the stock portfolio (calculated using a weighted average of the amounts put into the different stocks) while maintaining an expected return of at least 11%. Since future conditions may change, Michael has decided that no more than 35% of the portfolio should be invested in any one stock.

a. Help Michael formulate this as a linear program. (Hint: Define each variable as the proportion of the total investment that would be put in that stock. Include a constraint that restricts the sum of these variables to be 1.)

b. Help Michael solve this problem. What are the expected return and beta for this portfolio?