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
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter9: Decision Making Under Uncertainty
Section: Chapter Questions
Problem 46P
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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 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) = 
 
 
 
 
 
 
 
 
 
 
 
 
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ISBN:
9781337406659
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WINSTON, Wayne L.
Publisher:
Cengage,