4. Investment Advisors Lid. is a brokerage firm that manages stock portfolios for clients. A new client has requested that the firm handle an $80,000 investment portfolio. As an initial investment strategy, the client wants to restrict the portfolio to a mix of the following stocks: Stock: Price/share Estimated Annual Risk Index return per share per share Canadian Oil $25 $3 0.50 Hub Properties $50 $5 0.25 The risk index of the two investments represents a measure of the risk associated with investing in a particular stock; the higher the risk index, the greater the risk. By constraining the total risk for the portfolio, the investment firm avoids placing excessive amounts of the portfolio in potentially high-return, high-risk investments. For the current portfolio, an upper limit of 700 has been set for the total risk of all the investments. The firm has also set an upper limit of 1000 shares for the more risky Canadian Oil stock. Investment Advisors is trying to determine the number of shares of each stock they should be purchased to maximize the total annual return for their new client. The LP formulation is: 2 of 5 BUS 336 Review Max Profit = 3X1 + 5X2 Subject to: 25X1 + 50X2 $ 80,000 (total investment limit) 0.5X1 + 0.25X2 $ 700 (total risk index - cannot exceed) X1 $ 1000 (max. investment in Canadian Oil) X1 and X2 2 0 Using the LP output (the answer and sensitivity reports). answer the following questions: a) What is the optimal solution for Investment Advisors? b) Which constraints are binding? What is your interpretation of this condition in terms of the problem? C) Interpret the shadow price for the risk index constraint. d) Would it be beneficial to relax the constraint on the maximum amount that can be invested in Canadian Oil? Why or why not? ) How much would the estimated return per share for Canadian Oil have to increase before increasing the investment in this stock would be beneficial? Explain. f) Suppose the estimated annual return per share for Hub properties increased by $1.00. How do you expect the solution to change? g) By how much would the total annual return be reduced if the Canadian Oil maximum limit of 1000 shares investment be reduced to 900 shares? Microsoft Excel 16.0 Answer Report Target Cell (Max) Cell Name Original Value Final Value SD$2 MAXIMIZE PROFIT = 0 8400 Adjustable Cells Cell Name Original Value Final Value $B$5 Number of Share to invest in: Can. Oil 0 800 $C$5 Number of Share to invest in: Hub 0 1200 Constraints Cell Name Cell Value Formula Status Slack SD$9 Investment Limit Used (or LHS) 80000 SD$9=0 Not Binding 800 SC$5 Number of Share to invest in: Hub 1200 SC$5>=0 Not Binding 1200 Microsoft Excel 16.0 Sensitivity Report Adjustable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$5 Number of Share to invest in: Can. Oil 800 3 0.5 $C$5 Number of Share to invest in: Hub 1200 0 5 3.5 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $DS9 Investment Limit Used (or LHS) 80000 0.093333 80000 60000 15000 $D$10 Total Risk Used (or LHS) 700 1.333333 700 75 300 $D$11 Cdn Oil limit Used (or LHS) BOD 1000 1E+30 200