Question 3 (3 marks) A winner of a lottery has decided to invest $60,000 per year in the stock market. Under consideration are stocks for a petrochemical firm (X1) and a public utility (X2). Although a long-range goal is to get the highest possible return, some consideration is given to the risk involved with the stocks. A risk index on a scale of 1-10 (with 10 being the most risky) is assigned to each of the two stocks. The total risk of the portfolio is found by multiplying the risk of each stock by the dollars invested in that stock. The following table provides a summary of the return and risk: Stock Petrochemical Utility Estimated Return 15% 5% Risk Index 10 3 The investor would like to maximize the return on the investment, but the weighted risk index of the investment should not be higher than 7*. To formulate (but not solve) this problem as a linear program answer the following questions: * Hint: To find the weighted risk factor, multiply the amounts invested in each stock by the corresponding risk factor and sum then divide by the total investment a) Show the decision variables (0.5 mark) b) Show the objective function (0.5 mark) c) Show the constraints in standard form (i.e. suitable for using Excel's Solver)