1) In August 2011, Bank of Hawaii (BOH) stock cost $45 per share, yielded 4% per year in dividends, and had a risk index of 3.0 per share, while JPMorgan Chase (JPM) stock cost $40 per share, yielded 2.5% per year in dividends, and had a risk index of 2.0 per share.† You have up to $25,000 to invest in these stocks, and would like to earn at least $760 in dividends over the course of a year. (Assume the dividends to be unchanged for the year.) How many shares (to the nearest tenth of a unit) of each stock should you purchase to meet your requirements and minimize the total risk index for your portfolio? What is the minimum total risk index?
2) The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 740 homeless patients and no more than 900 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 2,400 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $9,700 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $7,700 per month. How many of each type of patient should it house in order to maximize profit?