Barbara Roberts recently received $30,000 as a small inheritance from a distant relative. She wants to invest the money so as to earn $900 to buy a notebook computer next year when she enters graduate school one year from now. (Barbara plans to use her inheritance to pay the tuition for her graduate studies.) She wants to create a portfolio using three stocks, whose annual percentage returns are summarized in the following table:

Barbara wants to diversify her potential holdings by investing at least $500, but no more than $20,000, in any one stock. Barbara wants to minimize the total variance (which also involves the covariance between the various pairs of stock) of the portfolio.
a. Formulate and solve a nonlinear programming model to determine how much money Barbara should invest in each stock to meet her financial goals. What is the optimal solution?
b. Will Barbara have enough money to buy a notebook computer nextyear?

Year Amalgamated Industries Babbage Computers Consolidated Foods 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 3.3 4.7 11.9 5.92 3.8 7.0 6.6 4.2 11.2 3.2 16.1 10.8 28.1 7.2 2.3 20.4 17.4 11.8 6.6 13.4 10.9 8.6 4.9 8.3