The government of Ghana has available GH1 billion earmarked for financing the Free SHS next year. Instead of letting this money sit in a bank account for a paltry 6% risk free interest rate, it has decided to invest half of the money in four stocks on the Ghana Stock Exchange (GSE). The four stock options the government is considering and the relevant financial data are as follows: Stock A B C D Price Per Share (in GH) 100 50 80 40 Annual Return (in GH) 18 6 8 8 Possible Loss Per Share (in GH) 10 6 6 5 However, the annual return is only a forecast (provided by experts at the ministry of finance), and could be worse or better a risk that the government has been advised to be worry of in order not to jeopardize the finances of the Free SHS program. For example, though a share of stock A could yield a return amount of GH18, it is also likely it could lead to a loss of GH10. In order to minimize the risk (i.e. losses) associated with investing on the GSE, the Finance Ministry has advised the government to adhere to the following guidelines: (1) The total forecasted annual return for the four stocks must be at least 9% of the total amount invested to justify the investment. Also, total possible losses must not exceed 8% of the total amount invested. (2) The amount invested in stock A and Stock C must not exceed GH200 million since when one performs better (worse) the other also performs better (worse). Likewise, the amount invested in Stock B and D must not exceed GH350 million for the same reason as that of Stock A and C. (3) Although Stock A carries a risk of a loss of GH10, the government is willing to buy at least 500,000 shares given the high return of GH18 per share. i. Formulate a linear program to determine the number of shares of each stock the government should buy in order to minimize the risk involve. Note that the government is not obliged to spend all the money intended for investment. (10 marks) ii. How many shares of each stock should be bought given the objective and the constraints, and what is the total possible loss that could occur? (5 marks) iii. Will the allocation change if the objective coefficient value for Stock B is decreased by GH3? Explain. (3 marks) iv. What will happen to the possible total loss if the total annual return requirement were to be raised by GH10,000,000? (4 marks) v. Interpret the reduce cost for Stock C. (