University of Florida football programs are printed $1$ week prior to each home game. Attendance averages $60,000$ screaming and loyal Gators fans, of whom two$-$thirds usually buy the program, following a normal distribution, for $$4$ each. Unsold programs are sent to a recycling center that pays only $20$ cents per program. The standard deviation is $10,000$ programs, and the cost to print each program is $$1.$ Refer to the standard normal table for $z-$values.

a$)$ What is the cost of underestimating demand for each program?

$C_s=$$$3\mathrm{.}00($round your response to two decimal places$).$

b$)$ What is the overage cost per program?

$C_0=$$$0\mathrm{.}80($round your response to two decimal places$).$

c$)$ How many programs should be ordered per game?

programs should be ordered per game $($round your response to the nearest whole number$).$

d$)$ What is the stockout risk for this order size?

Stockout risk $={0\mathrm{.}2105}^{TT}($round your response to four decimal places$).$