The Concession Stand at a Sporting Event Can Fill at Most

Essay

The concession stand at a sporting event can fill at most 12 orders per minute. If people arrive randomly at an average rate of $x$ people per minute, then the average wait $W$ in minutes before an order is filled is approximated by $W(x)=\frac{1}{12-x}$ where $0 \leq x<12$ .
(a) Evaluate $W(8), W(11)$ , and $W(11.9)$ . Interpret the results.
(b) Graph $W$ using the window $[0,12]$ by $[-.5,1]$ . Identify the vertical asymptote. What happens to $W$ as $x$ approaches 12 ?
(c) Find $x$ when the wait is 4 minutes.