Problem 1 - Knapsack Problem (10 points): A hedge-fund manager is considering 5 independent investment opportunities for a client. There is a fixed amount of $1,700,000 available to invest in a portfolio of these 5 opportunities. Each opportunity has an expected net return and requires an investment amount as shown in the following table: Opportunity Investment Amount ($) Expected Net Return ($) 1 2 3 4 5 400,000 600,000 300,000 500,000 800,000 100,000 180,000 60,000 200,000 400,000 (a) Assume that each opportunity requires full participation; partial participation is not allowed. The manager needs to determine the subset of opportunities to invest in, so as to maximize the total expected net returns subject to a budget constraint. Solve this problem as a Binary Program in Excel. (b) Assume that partial participation in each investment opportunity is allowed. In that case, we can invest a fraction of the money and receive the corresponding fraction of the expected net return. The manager needs to determine a portfolio of opportunities to invest in, so as to maximize the total expected net returns. Apply a step-by-step greedy algorithm to solve the corresponding lineal program. (c) Compare your solutions in (a) and (b).