1. (20 points) The finance division of NuTec is considering several investment options. If an option is selected, there is a minimium and maximum investment amount allowed. The relevant information is provided in the following table, with costs in million dollars. Minimum Maximum Expected Option Investment Investment Return (%) 234 123456 1 15 10 12 9 27 13 18 12 9 35 17 12 46 22 7 15 40 25 Because of the high risk nature of Option 6, company policy demands that the total amount invested in this option be no more than the total amount invested in Options 1, 2, and 3. For similar reasons, the total amount invested in Option 7 can be no more than the total amount invested in Options 1, 2, 3, and 4. Furthermore, if Option 6 is selected then Option 7 cannot be and vice versa. If Option 1 is selected then either Options 4 or 5 (or possibly both) must be selected. NuTec has $100 million available for investment. Formulate an integer linear program to determine which options to select in and how much should be invested in the selected options so as to maximize expected return based on the stated constraints. Be sure to define your variables and provide brief de- scriptive labels for your functional constraints.