answer all parts. correct answer shown. need work and step by step please.

You are on the committee planning for the upcoming Beta-Upsilon- Alpha-Delta (BUAD) Fraternity tailgate. Prior to the tailgate, you are responsible for purchasing beer. Someone else is buying water, soda and wine. The number of cans of beer to purchase depends on many factors - this game is between midterms and finals and the opponent is our rival UCLA Bruins, so you are expecting a great turnout. However, the weather that day will affect the number of cans of beer each fraternity member will drink: warmer temperatures mean they will drink more, but if it's too hot, fewer people will show up for the tailgate. You can assume you are able to purchase a beer at a cost of $3 per can and you will sell each can for $$. Left-over beer can be used at your next event, however since some seems to disappear at the frat house you can estimate the value at just 1/3 of the original cost. If you run out, your fellow fraternity members will be unhappy and may quit your fraternity, costing you future membership fees and decreased participation in events. This will cost your fraternity an average of $6 per can of desired beer by an upset member (in other words, if someone wanted 2 cans of beer, it would be a $12 cost to the fraternity). a) What is the cost to your fraternity if you don't buy enough beer? What if you buy too much beer? $11 if you don't buy enough $2 if you buy too much b) It's about a week before the game, and you hear the weather forecast will be between 75 and 80 degrees. Your roommate is majoring in Data Sciences. Based on past games and associated weather reports, he estimates the following beer demand for each temperature. How much beer should you order? 230 cans of beer c) Ignoring part b), it is now the day before the big game, so it looks like demand will be 200. Your Data Sciences roommate says that his beer demand could have a little error, so assume the demand is normally distributed with a standard deviation of 10 cans. You heard from the past that your Faculty Advisor was concerned about the backlash if we ran out of beer, and always wanted us to be 95% sure we did not run out beer. Following his guidance, how much should you order? 3 USC Marshall School of Business BUAD 311 Operations Management Fall 2022 216.4 cans of beer d) You found out the BUAD fraternity was just assigned a new faculty advisor who happens to teach BUAD 311. She told you that instead of aligning with the old advisor, use your Ops skills and determine the optimal amount of beer to order. You can assume the demand is still 200 cans with a standard deviation of 10. Now how much beer should you order