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 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 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 time-share properties; but they must agree to sit through a 2-hourproperty 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 2-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 a.m. to 10 p.m. daily with 4 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.

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 its phone reps $12 per hour. How many phone reps should it employ if it wants to maximize profit?