[Q4: Newsvendor] Your friend has just arrived from abroad and will be spending a month in the US. He wants to purchase a cell phone and a plan for the duration of his stay. Being students of Operations Management and experts at decision making you decide to help him find the cheapest plan, i.e., with the lowest expected payment. You narrow things down to two plans: - Plan A: Has a flat rate of $0.20 per minute used - Plan B: You can purchase talk time at the beginning of the month at the rate of $0.15 per minute. For each additional minute (beyond the purchased talk time) the rate is $0.50 per minute. For example, if you contract for 400 minutes, you first pay 400$0.15$60 at the beginning of the month. If you end up using 410 minutes during the month, you will have to pay (410400)0.50=$5 in addition to the $60. Your friend is quite chatty and forecasts his requirements for the phone for this month to be distributed as follows (he does not modify his usage based on his billi): a) What is the optimal number of minutes that should be contracted at the beginning of the month under Plan B? b) What is the expected payment for the month under Plan B if you contract for the minutes you computed in part a)? c) Which plan do you recommend to your friend and why