Will Rate if done properly and work is shown !!!

Problem 5: To celebrate the successful completion of their program, the class of 2020 are planning to go to the Sensation White Party in Amsterdam on July 2nd, 2021. Sensation White is mostly a trance and house event. All the attendees are required to wear white and the Amsterdam ArenA (this is the place where the event takes place) itself is decorated to match. Sensation White's slogan is "Be Part Of The Night - Dress in White". Every event has around 40,000- 45,000 tickets available (I am not making this up. It is from Wikipedia). Everybody is super excited about this party. You see this as an opportunity and decide to make some money by selling discounted tickets for those who want to go to the party. You contact the party organization committee in advance and find out that you can source tickets at a deep discount if you commit to buy in advance. Everybody can buy the tickets at the door for $100/ticket. However, you are planning to offer the tickets at a considerably lower price of $75/ticket. We'll assume that the students are rational so that if they plan to go to the party, they will buy tickets from you at $75 rather than paying $100 at the door. By surveying the class of 2020 and taking into account the fact that the students have hard time at the program and could not party much during the past school year, you figure out that demand for the party will be normally distributed with mean demand of 150 tickets and standard deviation of 50 tickets. The party organization committee informs you that there are two options to source the tickets for the party. Option 1: Preorder Tickets. You can preorder tickets one month ahead of the party as a one shot deal. You can get each ticket at a unit cost of $40/ticket. The organization committee also allows you to return any unsold tickets at $20/ticket. (a) How many tickets would you order in order to maximize your expected profit assuming that only option 1 is considered for the buying decision in this part of the question? Option 2: Reserve Tickets. Your second option is to reserve tickets at a cost of $10/ticket. That is, in addition to preordering tickets (option 1), you can also reserve some tickets by paying a non-refundable reservation fee of $10/ticket. If there is enough demand that all preorder tickets are sold, you will send the rest of the payment, which is $40 to the party organization committee, and you will get a permission to issue a ticket immediately. Note that the total cost of the ticket is increasing slightly (from $40 to $50) if the ticket is bought through reservation. You are selling the tickets for $75 as originally advertised. (b) (Extra Credit) How many tickets should you preorder (option 1) and how many tickets should you reserve (option 2) assuming that both options 1 and 2 are available to be used only as one-shot deals