L Use this statement to answer questions 1 to 6. The Delta Investment Company is considering seven investment opportunities (projects) that have varying capital requirements. The capital required for each investment and the net present value (NPV) each investment will generate are listed below. The total cash available for investment is $300,000. If Delta decides to invest in a project, it must incur the full investment cost and will enjoy the full NPV of that project. In other words, partial investment in any project is not possible. Delta wants to decide which investment opportunities (projects) to undertake in order to maximize its NPV. Investment Opportunity Capital Requirement NPV ($) ($) 1 70,000 120,000 2 85,000 145,000 3 92,000 160,000 4 45,000 75,000 5 62,000 105,000 6 30,000 48,000 7 76,000 130,000 Let y_i = 1 if Delta invest in investment opportunity i, and 0 otherwise, for i = 1, 2, ..., 7 Formulate and solve the problem to decide which projects to undertake to maximize NPV and write down the corresponding NPV. D Question 2 0.5 pts Suppose we have an additional restriction that we cannot undertake two specific projects together (i.e., if we undertake one of them, we cannot undertake the other). Which of the following statements is correct? O The NPV value with this restriction cannot be higher than the NPV without this restriction. The NPV can be smaller than, equal to, or larger than the NPV of the original solution depending on which two projects the restriction applies to. The NPV with this restriction will always be smaller than the NPV of the original solution regardless of which two projects the restriction applies to. O The restriction would not have an effect on the NPV. Question 3 0.5 pts Suppose that it is not possible to undertake all three projects 1, 3, and 5 simultaneously. Which of the below constraints would represent this restriction? Oy1+y3+ y5 = 1 y1+y3+y5 = 2 D Question 4 0.5 pts Suppose that it is not possible to undertake all three projects 1, 3, and 5 simultaneously, as was stated in the previous question. What is the NPV corresponding to the optimal solution when we impose this restriction? Question 5 0.5 pts Suppose in the original problem (ignoring the additional restrictions imposed in other questions), if Delta invests in Project 1, then it should also invest in Project 2. Which of the below constraints represent this requirement? O y1 y2>=0 O y1+ y2 >= 1 O y1 + y2 = 0 D Question 6 0.5 pts Suppose in the original problem (ignoring the additional restrictions imposed in other questions), if Delta invests in Project 1, then it should also invest in Project 2 (as in the previous question). What is the NPV corresponding to the optimal solution when we impose this restriction