You're an entry-level employee managing a financial portfolio. Because you're a total novice, your boss limits the portfolio to a single stock, and moreover, each day you're only allowed to make one

 You're an entry-level employee managing a financial portfolio. Because you're a total novice, your boss limits the portfolio to a single stock, and moreover, each day you're only allowed to make one of three choices: do nothing, purchase exactly one share, or sell all shares you currently own. You are scheduled to manage the portfolio for n days, and for each day i the price of the stock is estimated to be pi . Assume these estimations are perfect. On any given day i the value of your portfolio equals (#shares you own)pi−(amount spent to buy shares)+(amount made from selling past shares). (a) Devise a dynamic programming algorithm to determine the maximum value your portfolio can achieve on day n. Make sure to: • Clearly state your sub-problems in plain English • Formally define your sub-problems mathematically • State how one would arrive at the final answer from your sub-problems