$($Staffing Truck Drivers$)$ The US trucking industry suffers from notoriously high employee turnover, with turnover rates often well in excess of $100\%($Paz$$Frankel$,2006).$ This makes advance planning difficult since it is difficult to predict how many drivers will be available when needed. Suppose a trucking company needs $25$ drivers every day. If the company asks S drivers to report to work on a given day, the number of drivers who actually show up is given by images $,$ where images $.$ Drivers who report to work but are not needed must still be paid their daily wage of $$150.$ For each driver fewer than $25$ that show up$,$ the company will be unable to deliver a load, incurring a cost of $$1200.$ Find images $,$ the optimal number of drivers to ask to report to work. $($Fractional solutions are acceptable.$)$ Also report images $,$ the optimal expected cost per day.