1. 1. An investor is considering putting 100,000 in stocks of either an energy or manufacturing company. The goal is to generate long-term profit but he is also concerned about the risk exposure. He will be able to determine the risk for each company using a risk index scale of 1-12 (with 12 being the most risky). Total risk is computed by multiplying the risk of each stock by the amount invested in each. The energy company is expected to give a return of 10% with an assigned risk index of 8 while manufacturing’s return is 7% and a risk index of 3. The investor wants to maximize his profit but the average risk index should not be higher than 5. 
2. Solve the problem using linear programming. 
3. How much should be invested in each stock and the maximum return? 
4. What is the average risk for this investment?
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6. 2. The investor changed his perspective about the previous problem and wanted to emphasize instead investment risk. He now wants to minimize the risk of investment as long as a return of at least 6% is achieved. 
7. Formulate as an LP problem. 
8. How much should be invested in each stock and the maximum return? 
9. What is the average risk?