$1.[4$ points$]$ Consider a retailer that sells an item, which is replenished weekly from the supplier. The item sells for $$30/$unit and costs the retailer $$6/$unit$.$ The demand for the item follows a stochastic process, and, hence, the system may experience shortages or left over inventory at the end of each week. The retailer estimates that the loss$-$of$-$goodwill cost for shortages and the inventory holding cost for excess stock are $$5$ per unit and $$4$ per unit, respectively. The demand can assumed to be normally distributed with a mean of $100$ units per week and a standard deviation of $12$ units per week.