EXERCISE 7.15 (Investment Management under taxation) Last year, Ellen Grun- baum purchased s; shares of stock i at price qu i = 1, . . ., n. The current price per share of stock i is py i = 1, . . ., n. Ellen Grunbaum expects that the price per share of stock i one year from now will ber; i = 1, . . ., n. If she sells any shares, she must pay a trans- action cost of 1% of the amount transacted. In addition, she must pay a capital-gains tax at the rate of 30% on any capital gains at the time of the sale. For example, suppose that Ellen Grunbaum sells 1,000 shares of a stock today at $50 per share, which she had originally purchased at $30 per share. She would receive $50,000. However, she would have to pay capital gains taxes of 0.30 X (50,000 - 30,000) = $6,000, and she would have to pay 0.01 X (50,000) = $500 in transaction costs. There- fore, by selling 1,000 shares of this stock, she would have a net cashflow of $50,000 - $6,000 - $500 = $43,500. Now suppose that Ellen would like to sell enough shares of the stock in her portfolio today to generate an amount of cash C to- day for use as a down payment on a home. Formulate the problem of selecting how many shares of which stocks she needs to sell in order to generate the cash amount C, net of capital gains and transaction costs, while maximizing the expected value of her portfolio for next year