Reference no: EM133397569

A coffee cart opens at 7:00 am, and they generally try to prepare a batch large enough to accommodate their customers until 10:00 am, when the cart closes. The operator only sells 16 oz. servings, and each serving costs $0.50 to prepare, which includes all costs of production and any dairy/sweetener customers may add. Any coffee that isn't sold before 10:00 am is considered stale and disposed of for no monetary gain. When purchased, the coffee is poured into a ripple cup, which costs an additional $0.15 per cup. Demand over this period is normally distributed with a mean of 125 and a standard deviation of 35. Each cup retails for $2.75. The operator of the cart must also purchase a municipal license, which costs a flat $100 for the three hours. Assume there are no other costs associated with the cart. Develop a R model with 100,000 trials that simulates the daily profit resulting from the preparation of 75, 100, 120, 140, 160, and 180 servings of coffee a day (run them one at a time).

1. For each option, what is the expected profit, and which option results in the highest expected profit?

2. Create a histogram that displays the risk profile of profit for the number of servings with the highest expected profit.