1. Hiring Decision. Bruno and Ann Talotta are planning to open a small momandpop ice cream parlor specializing in homemade Gelato. Bruno and Ann have been told by all their friends that they make the best Gelato this side of Sicilia. Bruno plans to wait on customers while Ann prepares the Gelato and takes care of the general management of Luv I Talotta. Bruno and Ann are concerned about the length of time that their customers will have to wait in line. So, they are considering hiring a second person to help Bruno wait on customers. Bruno and Ann have spoken with their friends Sal and Lydia Bonaventura who own a Gelato shop in Spokane. Sal and Lydia have assured Bruno and Ann that customers do not like to wait for longer than two minutes before being served. Sal and Lydia have also noticed that customers arrival time at SalLyds approximates a Poisson distribution with a mean of 2.5 minutes (this indicates that on average one customer arrives every 2.5 minutes). They have also noticed that the number of minutes spent at the counter follows the frequency distribution below. (Lydia took some statistics and the University of Calabria in her youth.) The Talottas are trying to decide if they should hire counter help for Bruno. Bruno and Ann are sure that their customers would be upset if they had to wait more than two minutes. If a customer has to wait more than two minutes, he will renege, or leave to go, to the Dairy King on the next block. The average customer expenditure per visit has a triangular distribution with a minimum $3, most likely $8.00, and maximum of $15 per visit. The cost of hiring counter help for Bruno is $6.50 per hour including benefits. On a typical day Luv I Talotta serves customers from 11:00 a.m. to 9:00 p.m. Should Luv I Talotta hire an additional person to help Bruno at the counter? Carefully explain. 2. Retirement Planning. A recent MBA would like your assist- ance in determining how much to save for retirement. He is planning to invest $3,000 in a tax-sheltered retirement fund at the end of each year (i.e., appreciation of the fund is not taxed). The rate of return each year can be modeled as a normally distributed random variable with a mean of 12 percent and a standard deviation of 2 percent. a. If he is 30 years old now, how much money should he expect to have in his retirement fund at age 60? b. What is the probability that he will have more than $1 million in his retirement fund when he reaches age 60? c. How much should he invest each year if he wants the mean value of his portfolio to be at least $1 million at age 60? d. How much should he invest each year if he wants there to be a 90 percent chance of having at least $1 million in his retirement fund at age 60? Service Time Frequency Distribution Service Time Probability Minutes Distribution 1 0.225 2 0.325 3 0.275 4 0.150 5 0.015 6 0.010 Totals 1.000 2 3. Pricing Exotic Options. A given stock is currently priced at $100. Historically, its annual return has been 12 percent with a standard deviation of 15 percent. Build a spreadsheet simulation model for the stock price, using the option pricing model described in the text. Build the model to simulate the stock price over 126 days. Assume that the risk-free rate of return is 6 percent. a. A particular European call option gives the owner the right to purchase this stock after six months at a strike price of $105. What is the price of the option? b. Create a graph of the option price as a function of the strike price, for strike prices from $100 to $110 in increments of $1. c. A particular European put option gives the owner the right to sell this stock after six months at a strike price of $95. What is the price of the put? d. A lookback call option on this stock has an exercise price given by the minimum price observed over its six-month term. What is the price of the lookback option? e. An Asian option on this stock has a strike price set by the average value of the stock during its term. What is the price of the Asian option? f. A knockout call option on this stock terminates if the stock price reaches or exceeds $125 (that is, the option cannot be exercised). Otherwise, it has the same structure as the normal call. What is the price of the knockout option