Assume you are the artistic director of a music band that will have a concert in 6 months. The venue reserved for the concert has a capacity of 600 people. You want to sell some tickets in advance at the early-bird price and reserve some tickets for the day of the concert to be sold at the door (at a higher price of course!). Given that you want to maximize the revenue from ticket sales, how many tickets should you sell at the early-bird price, if the early-bird price is $40 and the door-price is $60? Assume the number of customers who prefer to buy their tickets at the door is normally distributed with mean 200 and standard deviation 50. Also assume you can fill up the venue by selling advance tickets but of course that wouldn't generate the highest possible revenue for you.