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 AGA Products Key Oil Price/Share $ 50 Estimated Annual Return (%) 6 100 10 The client wants to invest $40,000 and established the following two investment goals: Priority Level 1 Goal Goal 1: Obtain an annual retum of at least 9%. 1% Priority Level 2 Goal Goal 2: Limit the investment in Key Oil, the riskler investment, to no more than 60% of the total investment. Formulate a goal programming model for the DJS Investment problem. If you don't need the variable in the model, enter "o". If you need a negative number, enter minus sign with it. Let x2 = number of shares of AGA Products purchased X7 = number of shares of Key Oll purchased dit - the amount by which the annual return for the portfolio is greater than the target value dj = the amount by which the annual return for the portfolio is less than the target value dzt - 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(0;") + + P2d2+) s.t. + + X2 ≤ Funds available + + X2 + die + di Pi Goal + + X2 + dz + dz P2 Goal x1, x2, dat, di, d2t, d2 ≥ O 22 1000 1000 Number of shares of Key Oil purchased Number of shares of Key Oil purchased (200, 300) (200, 300) P2 Goal Funds available P2 Goal Funds available P1 Goal 1 0 1000 2000 Number of shares of AGA Products purchased PI Goal 0 21 1000 2000 Number of shares of AGA Products purchased (iii) (iv) 12 22 1000 1000 Number of shares of Key Oil purchased Number of shares of Key Oil purchased (200, 300) ( (200, 300) P2 Goal P2 Goal Funds available Funds available PI Goal P1 Goal 11 2000 0 1000 Number of shares of AGA Products purchased 0 21 1000 2000 Number of shares of AGA Products purchased