$6$ points$]$ Please report $4$ digits after the decimal for the critical ratio, $4$ digits after the decimal for the z$-$value, and $2$ digits after the decimal value for the quantity value.

For parts a through c$,$ you may use Excel to obtain the z values. However, please note that on the exam you will have to use the z$-$table to interpolate. Please make sure that you can solve this problem without using Excel too!

Consider a newsvendor model setting where the unit cost of having too much inventory is $$4/$unit and the cost of having too little inventory is $$10/$unit$.$ If the demand per period can assumed to be normally distributed with a mean of $100$ units per period and a standard deviation of $20$ per period.

a$.[2$ points$]$ What is the optimal order quantity for this setting?

b$.[2$ points$]$ Everything else being equal, what should the unit cost of overage be for the optimal order quantity to be $98$ units?

c$.[2$ points$]$ Everything else being equal, what should the unit cost of underage be for the optimal order quantity to be $120$ units?