a. On average, how many customers per hour does each sales person process?
b. What is the expected value of each call to VI’s toll free line?
c. Suppose VI pays it phone reps $12 per hour. How many phone reps should it employ if it wants to maximize profit?

Vacations Inc. (VI) markets time-share condominiums throughout North America. One way the company generates sales leads is by offering a chance to win a free mini-vacation to anyone who fills out an information card and places it in boxes that VI has distributed at various restaurants and shopping malls. All those who fill out the card and indicate an adequate income level subsequently receive a letter from VI indicating that they have indeed won the mini-vacation. To claim their prize, all the “winner” needs to do is call VI’s toll free number. When the “winner” calls the number, they learn that their mini-vacation consists of a free dinner, entertainment, and two-night stay at one of VI’s timeshare properties; but they must agree to sit through a two hour property tour and sales presentation.
About half the people who call VI’s toll free number to claim their prize wind up rejecting the offer after they learn about the two hour property tour. About 40% of those who call accept the mini-vacation and do the property tour but don’t buy anything. The remaining 10% of those who call the toll free number accept the mini-vacation and ultimately purchase a time-share. Each mini-vacation that VI awards costs the company about $250. Each sale of a time-share generates a net profit of $7,000 for VI after all commissions and other costs (including the $250 for the buyer’s mini-vacation) have been paid.
VI’s call center operates from 10 am to 10 pm daily with four sales representatives and receives calls at a rate of 50 per hour following a Poisson distribution. It takes an average of 4 minutes to handle each call with actual times being exponentially distributed. The phone system VI uses can keep up to 10 callers on hold at any time. Assume those who receive a busy signal don’t call back.