Johnston Investments is a financial services firm that manages funds for numerous clients. The company uses a proprietary asset allocation model that recommends the portion of each clients portfolio to be invested in exchange-traded fund, mutual fund and hedge fund. To maintain diversity in each clients portfolio, the firm places limits on the percentage of a portfolio that may be invested in each of the three funds, and assigns a limit on the portfolios risk index. A new client, Steve Richard should be advised on allocation of $600,000. Based on an evaluation of the clients risk tolerance, the Johnston Investments assigned a maximum risk index of .045 to the portfolio. The firms risk indicators show the risk rating for the exchange traded fund at .085, while the risk ratings for mutual fund and hedge fund are at .06 and .02 respectively. An overall portfolios risk index is computed as a weighted average of the risk rating for the three funds, where the weights are the fraction of the portfolio invested in each of the funds. Higher value of the risk index represents a more risky portfolio. Furthermore, to maintain diversity the fraction of Richards portfolio invested in exchange-traded and mutual fund must be at least 12% for each, and at least 25% of the total investment should be allocated to hedge funds. The firm is forecasting annual yields (returns) of 11% for the exchange-traded funds, 8.25% for mutual fund and 5.5% for the hedge fund. Based on the information provided, how should the new client be advised to allocate the $600,000 among the three funds to maximize the overall yield from the portfolio? Formulate a linear programming model for this portfolio selection problem (define decision variables, write down the objective function, develop constraints show all steps/calculations) and solve it using Excels Solver. Generate Answer report and sensitivity reports.