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 L

50

6

Key Oil

100

10

The client wants to invest $48,000 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 70% of the total investment.

(a) Formulate a goal programming model for the Varma Investment problem. (Let , be the number of shares of stock / purchased, d, pi be the deviation varlable which exceeds the value of goal 1, dni be

the deviation variable which is less than the value of goal I, for / = 1, 2.)

Min

+ P.

s.t.

Funds Available

P, Goal

P2

Goal

X,, dnind, I i 0 for / = 1, 2

(b) Use the graphical goal programming procedure to obtain a solution.

The client wants to imest $48,000 and established the foliowing two investrnent goals. Priority Level 1 Goal Gool 1: Obtain an annual return of at least 9%. Prisrity Level 2 Goal Goal 2: Limit the investment in Key os, the riskier investment, to no more than Jow of the total investment. the deviation variabie which is iess than the value of goal 10 for i=1,2.) Minp1()+p2( Funds Available 1Goalp2Goalxpdhrdpi0ford=1,2 (b) Use the graphical goal peogramming precedure to obtain a solutect. (x1,x2)=( The client wants to invest 340.000 and established the following two investment goais. Priority Level 1 Goul Goal 1: Obtain an arnual return of at least 9%. Priority Level 2 Goal Goal 2: Limit the investment in key Oi, the riskier investment, to no more than fow of the total investment. the deviation variable which is less than the value of poal i, for i=1,2.) MinF1()+P2( Funds Available pICoilP2GoilpdApdpN=0fori=1,2 (b) Use the praphical goal programening procedure to obtain a solutien. (x1;x2)=(