Verse Inc. sells virtual reality $($VR$)$ goggles, particularly targeting customers who like to play video games. Verse procures each pair of goggles for $$150$ from its supplier and sells each pair for

$$300.$ Monthly demand for the VR goggles is normally distributed with a mean of $160$ units and a standard deviation of $40$ units. At the beginning of each month, Verse orders enough goggles to

bring the inventory level up to $140$ goggles. If the monthly demand is less than $140,$ Verse pays $$20$ per goggles that remain in inventory. If the monthly demand exceeds $140,$ Verse sells only

the $140$ pairs in stock. There is shortage cost of $$40$ for each unit of demand that is unsatisfied to represent a "loss$-$of$-$goodwill" among its customers.

A$.$ Build a model to estimate the average monthly profit from the VR goggles.

B$.$ Run $1,000$ simulation trials to estimate the expected average monthly profit.

C$.$ Analyze the $1,000$ runs to determine what is the proportion of months in which demand is completely satisfied?

$*$ Could you please show how you did it on excel. Thank you.