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Varma 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 Price/Share($) Estimated AnnualReturn (%) AGA Products 1 50 6 Key Oil 2 100 10 The client wants to invest $38,000 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 Varma Investment problem. (Let xi be the number of shares of stock ipurchased, dp i be the deviation variable which exceeds the value of goal i, dn i be the deviation variable which is less than the value of goal i, for i = 1, 2.) Min P1 + P2 s.t. Funds Available P1 Goal P2 Goal xi, dn i, dp i ≥ 0 for i = 1, 2 (b) Use the graphical goal programming procedure to obtain a solution. (x1, x2) =

Practical Management Science

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section4.7: Financial Models

Problem 38P

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Varma 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	Price/Share ($)	Estimated Annual Return (%)
AGA Products 1	50	6
Key Oil 2	100	10

The client wants to invest $38,000 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 Varma Investment problem. (Let x_i be the number of shares of stock ipurchased, d_p i be the deviation variable which exceeds the value of goal i, d_n i be the deviation variable which is less than the value of goal i, for i = 1, 2.)

Min

P₁

+ P₂

s.t. Funds Available

P₁ Goal

P₂ Goal

x_i, d_n i, d_p i ≥ 0 for i = 1, 2

(b)

Use the graphical goal programming procedure to obtain a solution.

(x₁, x₂) =

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