Every year, you host a community concert where you sell commemorative T-shirts. The T-shirts feature images of that year's performers and typically only sell on the day of the concert. You order the T-shirts one month in advance of the concert and each T-shirt costs $8 to produce. On the day of the concert, you sell T-shirts at a price of $25 per shirt. After the day of the concert, you sell any unsold T-shirts to a local recycle shop for $5 each. From past years' historical sales, you predict the demand for T-shirts on the day of the concert will be as follows: X (in Shirts) 110 120 130 140 150
Probability that demand is exactly X 0.1 0.3 0.4 0.1 0.1

Required:
a. What are my underage and overage costs? Just by comparing these two costs, should we order more or less than the average demand? Briefly explain why.
b. How many T-shirts should I order to maximize my total expected profit?
c. If I order the quantity from part b, what is the likelihood that I stockout of T-shirts on the day of the concert?
d. If I order the quantity from part b, how many T-shirts do I expect to sell on the day of the concert?