NewCrest is looking to invest at most $500,000. The investment can be divided among three options. The return on each option depends on the economic outlook, which is shown in Table 1. For example, if the economic outlook is bright, investing $1 in option I will generate a gain of $3, and investing $1 in option II will result in a loss of $5. (a) (b) (c) Table 1: Return per dollar invested in the different options Return per dollar invested in option II -5 6 Economic outlook I 3 -2 Bright Gloomy III 7 -3 Axel, a business executive, proposed two alternatives to NewCrest. One is investing $100,000 in option I, $200,000 in II and $150,000 in III. The other is investing $60,000 in option I, $100,000 in II and $125,000 in III. NewCrest takes a conservative approach to decision-making. That is, it chooses the alternative that maximizes the minimum return produced by the two outcomes of the economic outlook. Discuss among the two alternatives proposed by Axel, which one NewCrest will choose. Please write clearly alternatives, states of nature and payoffs in a payoff table. Please limit the answer to within one page. (10 marks) Ben, another business executive, pointed out that NewCrest has an unlimited number of alternatives, not just the two proposed by Axel. Which alternative is best if New Crest takes a conservative approach to decision-making? To answer that question, Ben drafted, "Define x = investment in option I, x = investment in option II, and x3 = investment in option III. The objective is to Maximize min {3x - 5x2 + 7x3,-2x + 6x-3x3}". The objective function is not linear. Please search online "tricks to maximize the min of objective functions" or "transformations into linear programs". Then help Ben develop a complete Linear Programming (LP) model that represents the problem of deciding how much to invest in each option. Please limit the answer to within one page. (10 marks) Use the Excel Solver to find the optimal solution to the problem in Part (b) and summarise how NewCrest should invest. Please paste here three screenshots, (1) the problem worksheet just before clicking the Solver command, (2) the Solver Parameters dialog just before clicking Solve and (3) the Answer Report created by the Solver. Please limit the answer to within three pages. (20 marks)