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.