6 Financial Analysts Inc is an investment firm that manages

6 Financial Analysts, Inc., is an investment firm that manages stock portfolios for a number of clients. A new client has requested that the firm handle an $800,000 portfolio. As an initial investment strategy, the client would like to restrict the portfolio to a mix of the following two stocks: Stock Oil Alaska Southwest Petroleum Price/ Share $50 $30 Estimated Annual Return/Share $6 $4 Let x = number of shares of Oil Alaska y = number of shares of Southwest Petroleum Develop the objective function, assuming that the client desires to maximize the total annual return. Show the mathematical expression for each of the following three constraints: a. b. (1) Total investment funds available are $800,000 (2) Maximum Oil Alaska investment is $500,000 (3) Maximum Southwest Petroleum investment is $450,000 Note: Adding the. 0 and y 0 constraints provides a linear programming model for the investment problem. A solution procedure for this model will be discussed in Chapter 7

Solution

Answer to question a :

Total return from a share = Estimated annual return per share x Number of shares

Thus total estimated return from both shares , $ = 6x + 4.y

Thus object function :

Z = Maximize ( 6.x + 4.y)

X,Y > = 0

Answer to question b :

Total investment funds available is $800,000 :       50. X + 30.Y < = 800,000

Maximum Oil Alaska investment is $500,000 :     50. X < = 500,000, OR, X < = 10,000

Maximum Southwest petroleum investment is $450,000 : 30.Y < = 450,000, or, Y < = 15,000