EXAMPLE 2.6-26 (Portfolio Selection Problem) A leading Charted Accountant is attempting to determine the 'best'investment portfolio and is considering six alternative investment proposals. The following table indicates point estimates for the price per share, the annual growth rate in the price per share, the annual dividend per share and a measure of the risk associated with each investment. Portfolio data Shares under consideration B C DE F Current price/share) 100 160 120 150 200 Projected annual growth rate 0.07 0.10 0.12 0.09 0.15 Projected annual dividend per share ) 1.00 4.50 7.50 5.50 3.75 0.00 Projected risk in return 0.10 0.08 80 0.08 0.05 0.03 0.20 0,06 f18 The total amount available for investment is 25 lakhs and the following conditions are required to be satisfied.: (1) The maximum rupee amount to be invested in alternative F is 2,50,000. (iiNo more than 5,00,000 should be invested in alternatives A and B combined. (iii) Total weighted risk should not be greater than 0.10, where (Amount invested in alternative j) (risk of alternative j) total weighted risk = Total amount invested in all the alternatives (iv) For the sake of diversity, at least 100 shares of each stock should be purchased. (v) At least 10% of the total investment should be in alternatives A and B combined. (vi) Dividends for the year should be at least 10,000. Rupees return per share of stock is defined as price per share one year hence less current price per share plus dividend per share. If the objective is to maximize total rupee return, formulate the linear programming model for determining the optimal mumber of shares to be purchased in each of the shares under consideration. You may assume that the time horizon for the investment is one year. The formulated L.P. problem is not required to be solved. [C.A. Nov, 1991)