DJS Investment Services must develop an investment portfolio for a new client. A
ID: 2788146 • Letter: D
Question
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:
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.
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.
x2 = number of shares of Key Oil purchased
I already finished part of it, what about other blanks?
Estimated Annual Stock Price/Share Return (%) AGA Products $ 50 6 Key Oil 100 10Explanation / Answer
Total Investment = 40,000
Total value of Shares Already Purchased:
AGA Products (X1) = 50 * 50 = 2,500
Key Oil (X2) = 100 * 100 = 10,000
P1 GOAL:
D1 = Addtional shares purchased of AGA Products = 150 shares
D2 = Addtional shares purchased of Key Oil = 200 shares
Total investment in
AGA Products = (X1+D1) * Price = (50+150) * 50 = $10,000
Key Oil = (X2+D2)*Price = (100+200) *100 = $30,000
This investment structure will produce total return of 9 % for DJS invesrment services. To show,
AGA Products = $10,000 * Est annual return (6%) = $600
Key Oil = $30,000 = Est Annual return (10%) = $3000
Total Return = (3,600 / 40,000) * 100 = 9% total return
P2 GOAL: To limit Key Oil investment to maximum 60%
Investment in Key Oil to be reduced the Shares to 240 i.e ( X2(100)+D2 (200)- 60) . Value = 240 *100 = $24,000
Investment in AGA Products to be increased to 320 i.e ( X1(50)+D1(150)+120). Value = 320*50 = $16,000
Total Value = $40,000
Investment in Key Oil = (24,000/40,000) * 100 = 60%
Hope this elaborated answer helps.
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