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 ini- tial investment strategy, the client would like to restrict the portfolio to a mix of the fol- lowing two stocks:
Price/ Estimated Annual Stock Share Return/Share Oil Alaska $50 $6 Southwest Petroleum $30 $4
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Let x � number of shares of Oil Alaska y � number of shares of Southwest Petroleum
a. Develop the objective function, assuming that the client desires to maximize the total annual return.
b. Show the mathematical expression for each of the following three constraints: (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 x � 0 and y � 0 constraints provides a linear programming model for the investment problem.