please use R to show the whole process of calculation

A coffee cart opens at $7$:$00$ a$.$m$.,$ and they generally try to prepare a batch large enough to accommodate their customers until $10$:$00$ a$.$m$.,$ when the cart closes. The operator only sells $16$ oz$.$ servings and each serving costs $\backslash$$$0\mathrm{.}50$ to prepare, which includes all costs of production, and any dairy$/$sweetener customers may add. Any coffee that isn$$t sold before $10$:$00$ a$.$m$.$ is considered stale and disposed of for no monetary gain. When purchased, the coffee is poured into a ripple cup, which costs an additional $\backslash$$$0\mathrm{.}15$ per cup. Demand over this period is normally distributed with a mean of $125$ and a standard deviation of $35.$ Each cup retails for $\backslash$$$2\mathrm{.}75.$ The cart operator 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.$*$

$1.$ Write a function that takes as an argument the number of prepared servings in a day and returns a data frame where each row represents a different trial. The returned data frame should include randomly generated numbers for demand. Use these numbers and the information from the problem to calculate the cart$$s total revenue, cost, and profit for each trial as columns in the data frame.

$2.$ Use the function from part a to determine the cart$$s expected profit if the operator prepares $75,100,120,140,160,$ and $180$ servings. Which option results in the highest expected profit?

$3.$ Create a histogram that displays the risk profile of profit for the number of servings with the highest expected profit.