Digital currency such as Bitcoin has attracted many investors' attentions given its rapid growth of value very recently. Its superior return rate has also put pressure on many fund managers who are required to provide competitive return rates from their managed portfolios. Some fund managers have started to seriously consider including digital currency as part of their investment portfolios. However, they also know that such an investment decision can be highly risky since the price of digital currency is highly unstable. Janet Lopez is one of the fund managers who have done extensive research on digital currency. She estimates that the rate-of-return of digital currency is about 50%, i.e. 100 dollars of investment on digital currency can generate 50 dollars of profit, the coming year, whereas the rate-of-return of her current portfolio is 8%. She further estimates that the most she can lose in the next year in digital currency is 40%, i.e. 40% of any amount invested, whereas the most she could lose in her current portfolio is 10%. 

 

Janet is managing a $720,000 fund and needs to figure out how much to invest in digital currency and how much to invest in the existing portfolio so as to maximize the total profit. For risk management purpose, she has to limit the investment in digital currency to be no more than 25% of the total investment and also limit the potential loss of the total investment to be no more than $100,000. 

a. Formulate algebraically the Linear Programming (LP) model for this problem.

b. Solve this problem using the Graphical method: Identify the feasible region, then find the optimal solution(s) and optimal value for the LP model using the objective function line method. Describe also verbally how the manager should invest (i.e. Include "managerial statements" that communicate the results of the analyses)