Problem 14-02 (Algorithmic) ? DJS 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 Estimated Annual Return (%) 6 AGA Products $ 50 100 Key Oil 10 The client wants to invest $40,000 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 45% of the total investment. a. Formulate a goal programming model for the DJS Investment problem. If you don't need the variable in the model, enter "0". If you need a negative number, enter minus sign with it. Let x1 = number of shares of AGA Products purchased x2 = number of shares of Key Oil purchased d* = the amount by which the annual return for the portfolio is greater than the target value di the amount by which the annual return for the portfolio is less than the target value F d2+ = the amount by which the portfolio risk index exceeds the target value of the total investment d2 the amount by which the portfolio risk index is less than the target value of the total investment Min P1(d) + P2(d2+) s.t. X1 + X2 ≤ Funds available X1 + X2 + d = P1 Goal di++ + X1 + X2 + d2 d2 = P2 Goal x1, x2, di, di, d2, d2 ≥ 0 b. Choose the correct graph that solves the model formulated in part (a). (i) (ii) 1000+ r of shares of Key Oil purchased (200, 300) P2 Goal r of shares of Key Oil purchased 22 1000- (200, 300) / P2 Goal b. Choose the correct graph that solves the model formulated in part (a). (ii) (i) 22 1000- P2 Goal (iii) Number of shares of Key Oil purchased Number of shares of Key Oil purchased 0 22 1000+ 0 (200, 300) Funds available Pl Goal 1000 Number of shares of AGA Products purchased P2 Goal (200, 300) Funds available Pl Goal 1000 Number of shares of AGA Products purchased 21 2000 2000 (iv) 22 1000+ Number of shares of Key Oil purchased Number of shares of Key Oil purchased 0 22 1000+ 0 (200, 300) Funds available Pl Goal 1000 Number of shares of AGA Products purchased P2 Goal (200, 300) P2 Goal Funds available PI Goal 1000 Number of shares of AGA Products purchased 1 2000 21 2000