When Sally Mutton arrives at the bank, 30 minutes remain on her lunch break. If Sally makes it to the head of the line and enters service before the end of her lunch break, she earns reward r. However, Sally does not enjoy waiting in lines, so to reflect her dislike for waiting in line, she incurs a cost c for each minute she waits. During a minute in which n people are ahead of Sally, there is a probability p(x|n) that x people will complete their transactions. Suppose that when Sally arrives, 20 people are ahead of her in line. Use dy namic programming to determine a strategy for Sally that will maximize her expected net revenue (reward - waiting costs).