Problem $5.$ One Target store orders milk in $1$ gallon package using newsvendor$$s model. The demand for the milk follows a normal distribution and the average is $150$ units, with a standard deviation of $60$ units during each order cycle. The retail price of the milk is $$3$ per unit, and the cost for Target is $$2$ per unit. Target will mark those left$-$over milk near their expiration date down for $$1\mathrm{.}5$ per unit as special sales and Target is always able to sell all the left$-$over milk during those special sales. $(24$ points$)$

Question $7.$ Assuming this Target store orders $250$ units, what is the expected on$-$hand inventory? $($Please keep at $4$ decimal places$)$