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 Funds available available Pl Goal Pl Goal C1 C1 O 1000 2000 0 1000 2000 Number of shares of AGA Products purchased Number of shares of AGA Products purchased (iii) (iv) 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 Funds available available Pl Goal Pl Goal 0 1000 2000 0 1000 2000 AGA Pro fAGA ProProblem 14-02 (Algorithmic) D15 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: Estimated Annual Stock Price/Share Return (as) AGA Products 5 so 6 Key on 100 10 The client wants to invest $40,000 and established ie following two investment goals: Pn'on'ty 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 invatment. a. Formulate a goal programming model for the D15 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 x; = number of shares ofAGA Products purchased x2 = number of shares of Key Oil purchased (11* = the amount by which the annual return for the portfolio is greater than the target value d1' = the amount by which the annual return for the portfolio is less than the target value (12* = the amount by which the portfolio risk index exceeds the target value of the total investment dz' = the amount by which the portfollo rlsk Index Is less than the target value of the total Investment Funds available x1, x2, :11". d1', d2+, :12 "