2. [60 points] You are evaluating options for purchasing cloud computing resources. There are two plans. Plan A: Has a flat rate of $20 per hour used. Plan B: You can purchase computing time at the beginning of the month at the rate of $15 per hour. For each additional hour (beyond the purchased time) the rate is $50 per hour. For example, if you contract for 100 hours, you first pay 100*$15=$1500 at the beginning of the month. If you end up using 110 hours during the month, you will have to pay (110-100)*50=$500 in addition to the $1500. You forecast your computing resource requirements for next month to be distributed as follows (you do not modify your usage based on this bill!): Hours Probability Cumulative 200 0.1 0.1 400 0.3 0.4 600 0.4 0.8 800 0.2 1.0 a. What is the optimal number of hours that should be contracted at the beginning of the month under Plan B? (Hint: Identify the overage and underage costs.) b. What is the expected payment for the month under Plan B if you contract for the hours you computed in part a? c. What is the expected payment for the month under Plan A if you contract for the expected number of hours that you will use? d. Which plan will you choose