Problem 14-02 (Algorithmic) DJS Investment Services must develop an investment p

Question

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 Stock AGA Products Key Oil Price/Share Return (%) 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 50 x 400Funds available 10x2 0 x1, x2, di, d1,d2,d2 2 0

Explanation / Answer

Second constraint

6 x (50x1) + 10 (100x2) 9 x 40,000
or, 300x1 + 1000x2 360,000
or, 3x1 + 10x2 3600

i.e. 3x1 + 10x2 - d1+ + d1- = 3600

Third Constraint

0 x (50x1) + 1 x (100x2) 0.6 x 40,000
or, 0x1 + 100x2 24,000
or, 0x1 + 1x2 240

or, 0x1 + 1x2 - d2+ + d2- = 240

-----------------------------------------------------------------------------------------------------------------------

Note that, strictly speaking, the above formulations are unacceptable because in the RHS, we cannot write 40,000 directly. Istead, we need to write the actual fund consumed i.e. (50x1 + 100x2). So, the actual constraints should look like -

6 x (50x1) + 10 (100x2) 9 x (50x1 + 100x2) i.e. -150x1 + 100x2 0 i.e. -3x1 + 2x2 - d1+ + d1- = 0 ----(2)
0 x (50x1) + 1 x (100x2) 0.6 x (50x1 + 100x2) i.e. -30x1 + 40x2 0 i.e. -3x1 + 4x2 - d2+ + d2- = 0 ----(3)

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---