You've graduated from college, landed a great job, and are ready to invest some of your income. Understanding that a diversified portfolio, that is, not putting all of your eggs in one basket, is an important part of any investment strategy, you decide to split your money between two mutual funds. Your main goal is, of course, to earn as much money on your investments as possible, but you also know that there is risk involved in trading on the stock market. How do you balance your investments in order to maximize return and minimize risk? In this project, we will use linear programming to analyze and attempt to answer these questions. Work through the questions below to set up and solve a linear programming scenario that addresses this problem, and report back on your group's results. 1. Choose two mutual funds to purchase. Search for two mutual funds that you are interested in investing in and use the Fidelity and Yahoo Finance websites to find the following information (we will walk through it in class together):  Performance. Identify the 5-Year Total Return % of each investment fund. You will use this to estimate your return going forward. For this project, we will require that each fund has at least five years of data.  Risk. Identify the 5-Year Standard Deviation statistic of each fund. This number represents the volatility of the fund's returns, and hence may be used to measure the risk of losing money on your investment.  Price. Identify the Minimum Initial Investment amount for each fund. For this project, we will require this amount to be non-zero. 2. Write the objective functions. For this project, we will construct two separate objective functions: one to maximize return and one to minimize risk.  Define the variables  and  as the amounts to be invested in each mutual fund.  Use the information you gathered on the funds' performance to construct an objective function for the total expected return on your investment.  Use the information you gathered on the funds' risk to construct an objective function for the total risk involved in purchasing both funds. We will use a calculation of Std. Dev. multiplied with the Amount to measure the risk of purchasing shares of a fund (higher Std. Dev. means higher risk). 3. Identify your constraint inequalities. Form constraint inequalities by considering the following limitations on your investment.  The minimum amount needed to start investing in each fund.  The maximum total amount that you have available to invest (your choice on this one). To ensure a good range for your results, choose a reasonable number that is at least twice as much as the total minimum amount to purchase the two funds.  To maintain an appropriately diversified portfolio, suppose you intend that the difference between the amounts invested in each fund be no more than 25% of the maximum total amount (if you have questions about how to represent this let me know). 4. Graph the feasible region. Using either graph paper or a computer graphing application, plot the feasible region, including all of the following:  An appropriate chart title and label for each line graphed.  Scale of both axes. (How much does each tick mark on the graph represent?)  Shading in the feasible region only (not all the massive regions shaded) and clearly marked and labeled corner points.