FORMULATE THE LINEAR PROGRAMMING

A leading financial analyst is attempting to determine a 'best' investment proposal and is considering six alternatives investment proposals. Table 1 indicates the point estimates for the price per share, the annual growth in the price per share, the annual divided per share, and the measure of the risk associated with each investment Description Share A B D E F 80 100 160 120 150 200 0.08 0.07 0.1 0.09 0.15 Current price per share (RM) Projected annual 0.12 growth rate Projected dividend per 5.50 share (RM) Projected risk in return 0.05 0.03 0.2 Table 1: Data on returns on investment in various share 4.00 4.50 7.50 5.75 0.00 0.10 0.06 0.08 The total amount available for investments is RM 2.5 Millions and the following additional conditions are required to be satisfied a) The maximum amount to be invested in alternative Fis RM 250,000. b) No more than RM 500,000 should be invested in alternatives A and B combined. c) Total weighted risk should not be greater than 0.1 where, (Amount invested in alternative j) (Risk of alternative j) Total weighted risk = (Total amount invested in all alternatives) d) A minimum of 100 share should be purchased for each share option. e) At least 10% of the total investments should be in alternatives A and B combined. f) Dividends for the year should be at least RM 10,000. Return per share is defined as the purchased price of one share less current price at the end of the year plus dividend per share. Formulate the LP model and find the optimal number of shares to be purchased in each of the shares under consideration if the objective is to maximize total return