Varma Investment Services must develop an investment portfolio for a new client. As an initial investment strategy, the new client would like to restrict the portfolio to a mix of two stocks. Stock Price/Share ($) 1 AGA Products 50 2 Key Oil 100 Estimated Annual Return (%) 6 10 The client wants to invest $48,000 and established the following two investment goals. Priority Level 1 Goal Goal 1: Obtain an annual return of at least 9%. Priority Level 2 Goal Goal 2: Limit the investment in Key Oil, the riskier investment, to no more than 60% of the total investment. pi (a) Formulate a goal programming model for the Varma Investment problem. (Let x, be the number of shares of stock i purchased, do; be the deviation variable which exceeds the value of goal i, dni be the deviation variable which is less than the value of goal i, for i = 1, 2.) Min P + P. s.t. Funds Available P1 Goal P Goal xdni di 0 for / = 1, 2 (b) Use the graphical goal programming procedure to obtain a solution. (x1, x2)=