why it is wrong? Problem 14-02 (Algorithmic) DJS Investment Services must develo

Question

why it is wrong?

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: Estimated Annual Return (%) Stock AGA Products Key Oil Price/Share s 50 100 10 The client wants to invest $40,000 and established the following two investment goals: Priority Level 1 Goal Goal 1: Obtain an annual 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. a. 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 x1 = number of shares of AGA Products purchased X2 = number of shares of Key Oil purchased Min 1P2(d2+ Funds 50 X1 100 X2 10 X2 100 X2 40000 available 3600 P1 Goal 24000 P2 Goal 0 X1 x1, x2, d1, d1, d2, d2 2 0

Explanation / Answer

Goal 1 is priority level 1. Therefore, we need to attach higher prior number to that

So objective is: Min 2*P1(d1-) + 1*P2(d2+)

s.t.

50*x1 + 100*x2 <= 40000 Funds available

50*0.06*x1 + 100*0.10*x2 -1*d1+ + 1*d1- = 0.09*(50*x1 + 100*x2) P1 goal

100*x2 -1*d2+ + 1*d2- = 0.60*(50*x1 + 100*x2) P2 goal

P1 and P2 goal constraints can be rewritten in simple form as follows

-1.5*x1 + 1*x2 -1*d1+ + 1*d1- = 0   P1 goal

-30*x1 + 40*x2 -1*d2+ + 1*d2- = 0   P2 goal

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