19 The Paris Bakery has decided to bake 30 batches of its famous beignets at the beginning of the day. The store has determined that daily demand will follow the distribution shown in the following table:

DAILY DEMAND PROBABILITY 15 0.08 20 0.12 25 0.25 30 0.20 35 0.20 40 0.15 Each batch costs the Paris Bakery $50 and can be sold for $100. The Paris Bakery can sell any unsold batches for $25 the next day.

(a) Simulate 1 month (25 days) of operation to calculate the bakery’s total monthly profit. Replicate this calculation N times to compute the average total monthly profit.

(b) The Paris Bakery would like to investigate the profitability of baking 25, 30, 35, or 40 batches at the start of the day. Which quantity would you recommend? Why?