a. Diners queue at a busy fast-food restaurant at an average rate of 10 customers per hour, while restaurant staff can serve one customer every 5 minutes. i. Calculate the average number of customers waiting in the queue. ii. Calculate the average number of minutes a customer waits in the queue. b. An independent film company is about to release a new movie. For the initial release, the movie could be shown in theatres, be made available via a streaming service, or go direct to DVD. Market research of a sample of test audiences has found that interest in the new movie can be classified as either high, medium or low, with probabilities 0.3,0.5 and 0.2 , respectively. The projected profits in millions of dollars for each release mode are summarised in the following table: i. Calculate the expected profit in millions of dollars for each alternative, and state which one the company should choose to maximise the expected profit. ii. The regret table for the problem is: Calculate the expected regret for each alternative and state which one the company should choose to minimise the expected regret. Is it the same alternative that was chosen in part (i)